#### Answer

$x=1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2x-1=\log_6 6^x
,$ use the properties of logarithms. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
2x-1=x\log_6 6
.\end{array}
Since $\log_b b =1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
2x-1=x(1)
\\\\
2x-1=x
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
2x-x=1
\\\\
x=1
.\end{array}