Logarithms

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Problem #1
What is the value of [tex] \log_{\frac{1}{4}} 8\sqrt[3]{2} [/tex]?

Problem #2
What is the value of [tex] \log_4 \sqrt{2} +\log_{\sqrt{8}} 2 [/tex]?

Problem #3
[tex] 3^{\log_3 1}+x^{\log_4 2} =3 [/tex]
Find [tex]x[/tex]?

Problem #4
Let [tex] 9^x=3\sqrt{3} [/tex]
What is the value of [tex] \log_2 (1-x) [/tex]?

Problem #5
[tex] \log_{15} 2 = \alpha [/tex] and [tex] \log_{15} 3= \beta [/tex]
What is the value of [tex] \log_{\sqrt{15}} 100 [/tex]?

Problem #6
[tex] \log_{10} (x^2-9)=\log_{10} (x+3) +2 \log_{10} 3[/tex]
What is the value of [tex] x [/tex]?

Problem #7
[tex]\log_x (2x-3)+\log_x 3=2 [/tex]
What is the value of [tex] \log_8 (x^2+6.5) [/tex]?

Problem #8
[tex]\log_{10} (x^2-11)=1+\log_{10} x [/tex]
What is the value of [tex] \log_{10} (x-1)[/tex]?

Problem #9
[tex]\log_3 x +\log_x 9 =3[/tex]
What is the value of [tex] \log_{\sqrt{3}} x [/tex]?




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