#### Answer

$x=0$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}