## College Algebra (11th Edition)

$x=0$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $12^x=1 ,$ take the logarithm of both sides. Use the properties of logarithms and of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the logarithm of both sides results to \begin{array}{l}\require{cancel} \log12^x=\log1 .\end{array} 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} x\log12=\log1 \\\\ x=\dfrac{\log1}{\log12} .\end{array} Since $\log1=0,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x=\dfrac{0}{\log12} \\\\ x=0 .\end{array}