Answer
$\displaystyle \frac{4}{5}$
Work Step by Step
Basic Logarithmic Properties
1. $\log_{b}1=0$
2. $\log_{b}b=1$
3. $\log_{b}b^{x}=x$
4. $b^{\log_{b}x}=x$
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Term by term:
$\log_{3}81=\log_{3}3^{4}=4\qquad $...(3)
$\log_{\pi}1=0\qquad $...($1$)
$2\sqrt{2}=\sqrt{2^{2}\cdot 2}=\sqrt{8}$
$8=(\sqrt{8})^{2}$, so
$\log_{\sqrt{8}}(8)=\log_{(\sqrt{8})}(\sqrt{8})^{2}=2\qquad $...(3)
$\log 0.001=\log 10^{-3}=-3\qquad $...(3)
Problem expression$=\displaystyle \frac{4-0}{2-(-3)}=\frac{4}{5}$
