Answer
$0.8$
Work Step by Step
For $a>0, a\neq 1$, and $x>0,\qquad y=\log_{a}x$ means $a^{y}=x$.
$.................................$
$\log_{32}16=x$ means $32^{x}=16$,
$32^{x}=16$
$(2^{5})^{x}=16$
$2^{5x}=2^{4}\qquad \color{blue}{\text{ ...equate the exponents } }$
$5x=4$
$x=\displaystyle \frac{4}{5}=0.8$
With change of base, $\displaystyle \log_{a}x=\frac{\log_{b}x}{\log_{b}a}=\frac{\ln x}{\ln a}$,
using a calculator,
$\log_{32}16$=$\displaystyle \frac{\ln 16}{\ln 32}=0.8$
