Question

Solve the following logarithmic equation.
2log(base6)(x-5)+log(base6)(9)=2
x=__________________
OR
There is no solution.

Answer 1

\[
2\log_6(x-5)+\log_6(9)=2 \\
\log_6((x-5)^2)+\log_6(9)=2 \\
\log_6(9(x-5)^2)=2 \\
6^{\log_6(9(x-5)^2)} =6^2 \\
9(x-5)^2=36
\]

Answer 2

thank you super much!