we have the equation
[tex]23^x=6[/tex]Remember the definition of logarithm
[tex]\begin{gathered} If \\ a^x=b \\ then \\ x=\log_ab \end{gathered}[/tex]Applying the definition of a logarithm to this problem
we have that
[tex]x=\log_{23}6[/tex]Apply change of base formula
Remember that
[tex]\log_bM=\frac{\log_{10}M}{\log_{10}b}=\frac{logM}{logb}[/tex]so
[tex]\log_{23}6=\frac{log6}{log23}[/tex]therefore
The answer is
[tex]x=\frac{log6}{log23}[/tex]