# Hard logarithm problem HELP!

Logarithms problems.

### Hard logarithm problem HELP!

Greetings, I was learning logarithms when I found this problem(pls see attachment) and it ask me to simplify it, but i have not found yet an explanation on how to solve it.
Could you please provide tips or an explanation as to how to solve this problem(and the steps if possible) please?
The help is appreciated.
Thank you.
Attachments
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Learningforcomp

Posts: 9
Joined: Fri Sep 11, 2020 2:35 pm
Reputation: 0

### Re: Hard logarithm problem HELP!

Good afternoon!

Look for 'change of base'.
$$\log_b(a)=\frac{\log_c{a}}{\log_c{b}}$$

So:
$$\log_{x_2}\,x_1\cdot\log_{x_3}\,x_2\cdot\ldots\cdot\log_{x_n}\,x_{n-1}=\frac{\log\,x_1}{\log\,x_2}\cdot\frac{\log\,x_2}{\log\,x_3}\cdot\ldots\cdot\frac{\log\,x_{n-1}}{\log\,x_n}=\frac{\log\,x_1}{\log\,x_n}=\log_{x_n}\,x_1$$

Baltuilhe

Posts: 65
Joined: Fri Dec 14, 2018 3:55 pm
Reputation: 44

### Re: Hard logarithm problem HELP!

Baltuilhe wrote:Good afternoon!

Look for 'change of base'.
<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>b</mi></msub><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>c</mi></msub><mi>a</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>c</mi></msub><mi>b</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \log_b(a)=\frac{\log_c{a}}{\log_c{b}}</annotation></semantics>[/itex]</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 1em; vertical-align: -0.25em;"></span><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.241968em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.24414em;"><span class=""></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">a</span><span class="mclose">)</span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 2.30158em; vertical-align: -0.93014em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.37144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.24414em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.24414em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.93014em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>

So:
<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><msub><mo><mi>log</mi><mo>⁡</mo></mo><msub><mi>x</mi><mn>2</mn></msub></msub> <msub><mi>x</mi><mn>1</mn></msub><mo>⋅</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><msub><mi>x</mi><mn>3</mn></msub></msub> <msub><mi>x</mi><mn>2</mn></msub><mo>⋅</mo><mo>…</mo><mo>⋅</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><msub><mi>x</mi><mi>n</mi></msub></msub> <msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mn>1</mn></msub></mrow><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mn>2</mn></msub></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mn>2</mn></msub></mrow><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mn>3</mn></msub></mrow></mfrac><mo>⋅</mo><mo>…</mo><mo>⋅</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mn>1</mn></msub></mrow><mrow><mi>log</mi><mo>⁡</mo> <msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac><mo>=</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><msub><mi>x</mi><mi>n</mi></msub></msub> <msub><mi>x</mi><mn>1</mn></msub></mstyle></mrow><annotation encoding="application/x-tex">\displaystyle \log_{x_2}\,x_1\cdot\log_{x_3}\,x_2\cdot\ldots\cdot\log_{x_n}\,x_{n-1}=\frac{\log\,x_1}{\log\,x_2}\cdot\frac{\log\,x_2}{\log\,x_3}\cdot\ldots\cdot\frac{\log\,x_{n-1}}{\log\,x_n}=\frac{\log\,x_1}{\log\,x_n}=\log_{x_n}\,x_1</annotation></semantics>[/itex]</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 1.03868em; vertical-align: -0.34424em;"></span><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.317314em;"><span class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.143em;"><span class=""></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.34424em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 1.03868em; vertical-align: -0.34424em;"></span><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.317314em;"><span class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.143em;"><span class=""></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.34424em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 0.44445em; vertical-align: 0em;"></span><span class="minner">…</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 1.03868em; vertical-align: -0.34424em;"></span><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.164543em;"><span class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.143em;"><span class=""></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.34424em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.208331em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 2.25188em; vertical-align: -0.88044em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.37144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.88044em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 2.25188em; vertical-align: -0.88044em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.37144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.88044em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 0.44445em; vertical-align: 0em;"></span><span class="minner">…</span><span class="mspace" style="margin-right: 0.222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right: 0.222222em;"></span></span><span class="base"><span class="strut" style="height: 2.25188em; vertical-align: -0.88044em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.37144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.208331em;"><span class=""></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.88044em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 2.25188em; vertical-align: -0.88044em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.37144em;"><span class="" style="top: -2.314em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span><span class="" style="top: -3.23em;"><span class="pstrut" style="height: 3em;"></span><span class="frac-line" style="border-bottom-width: 0.04em;"></span></span><span class="" style="top: -3.677em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.88044em;"><span class=""></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right: 0.277778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.277778em;"></span></span><span class="base"><span class="strut" style="height: 1.03868em; vertical-align: -0.34424em;"></span><span class="mop"><span class="mop">lo<span style="margin-right: 0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.057252em;"><span class="" style="top: -2.45586em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.164543em;"><span class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.143em;"><span class=""></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.34424em;"><span class=""></span></span></span></span></span></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mspace" style="margin-right: 0.166667em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span></span>
Thank you Baltuilhe. I was able to understand and find the answer, I deeply appreciate your help.

Learningforcomp

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