Answer
$y\approx 0.9534$
Work Step by Step
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=9, y=2y, x=66$), we get:
$\log_{9}{66}=2y$
Next, recall the change of base formula (pg. 464):
$\log_{b}{m}=\dfrac{\log_{c}{m}}{\log_{c}{b}}$
Applying this formula to our last equation, we get:
$\log_{9}{66}=2y$
$\dfrac{\log_{10}{66}}{\log_{10}{9}}=2y$
$\dfrac{1}{2}\cdot \dfrac{\log_{10}{66}}{\log_{10}{9}}=y$
$y\approx 0.9534$
We confirm that the answer works:
$9^{2\cdot 0.9534}=66$
$9^{1.9068}=66$
$66=66$
