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Solve for x
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Re: Solve for x
by Eigenvalue » Fri Oct 02, 2026 9:55 pm
Rewrite [tex]\frac{27}{8}[/tex] as [tex]\frac{3³}{2³}[/tex], and by extension ([tex]\frac{3}{2}[/tex])³
([tex]\frac{3}{2}[/tex])³=[tex]( \frac{2}{3})^{-3}[/tex]
[tex]( \frac{2}{3})^{-3}[/tex]=[tex]( \frac{2}{3})^{x+2}[/tex]
As the bases are equal and the expressions are equal, the bases are equal
-3=x+2
x=-5
([tex]\frac{3}{2}[/tex])³=[tex]( \frac{2}{3})^{-3}[/tex]
[tex]( \frac{2}{3})^{-3}[/tex]=[tex]( \frac{2}{3})^{x+2}[/tex]
As the bases are equal and the expressions are equal, the bases are equal
-3=x+2
x=-5
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Re: Solve for x
by nycmath » Sat Oct 03, 2026 6:45 pm
Eigenvalue wrote:Rewrite [tex]\frac{27}{8}[/tex] as [tex]\frac{3³}{2³}[/tex], and by extension ([tex]\frac{3}{2}[/tex])³
([tex]\frac{3}{2}[/tex])³=[tex]( \frac{2}{3})^{-3}[/tex]
[tex]( \frac{2}{3})^{-3}[/tex]=[tex]( \frac{2}{3})^{x+2}[/tex]
As the bases are equal and the expressions are equal, the bases are equal
-3=x+2
x=-5
When the bases are equal, we equate the exponents.
Re: Solve for x
by Eigenvalue » Sat Oct 03, 2026 10:00 pm
I meant for the reply to say "As the bases are equal and the expressions are equal, the exponents are equal"; there was a typo
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