## College Algebra (11th Edition)

$x=1$
$\bf{\text{Solution Outline:}}$ 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}