Answer
$1.262$
Work Step by Step
Using change-of-base, $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$, we change base to 10
$\displaystyle \log_{9}16=\frac{\log 16}{\log 9}$
... next, we recognize $16=2^{4},\ 9=3^{2}$
... and apply $\log_{a}M^{p}=p\cdot\log_{a}M$.
$... =\displaystyle \frac{4\log 2}{2\log 3}$
... substitute $\log 2=0.301$ and $\log 3=0.477,$
$=\displaystyle \frac{4\times 0.301}{2\times 0.477}\approx$1.26205450734
To three decimal places,
$=1.262$
