Answer
$x \approx 0.613$
Work Step by Step
Re-write the first term as:
$36^x=(6^{2})^{x}=(6^{x})^{2}$
We wish to substitute $a=6^{x}$, so the equation becomes:
$a^{2}-6a+9=0 $
This gives a quadratic equation, whose factors are: $(t-3)^2=0$
Use the zero factor property to obtain: $ t- 3 =0 \implies t= 3$
Therefore, $6^{x}=3$
or, $x= \log_6 3 \approx 0.613$
Thus, our answer is: $x \approx 0.613$
