Solution
[tex]log_x(9)=2[/tex]
Apply log rule
[tex]\frac{1}{\log _9\left(x\right)}=2[/tex]
To clear the fraction multiply both sides by the L C M
[tex]\frac{1}{\log _9\left(x\right)}\log _9\left(x\right)=2\log _9\left(x\right)[/tex]
Simplify
[tex]1=2\log _9\left(x\right)[/tex][tex]\begin{gathered} \frac{2\log _9\left(x\right)}{2}=\frac{1}{2} \\ \\ \end{gathered}[/tex]
Simplify
[tex]\log _9\left(x\right)=\frac{1}{2}[/tex]
Apply log rule
[tex]x=3[/tex]
Another method (convert the equation into the exponential form)
[tex]\begin{gathered} \:log_x\left(9\right)=2\: \\ \\ \:x^2=9 \\ x^2=3^2 \\ \\ x=3 \end{gathered}[/tex]
