Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set - Page 811: 91

$\displaystyle \frac{2}{5}$

LHS: apply$\qquad \log_{a}(MN)=\log_{a}M+\log_{a}N$ RHS: apply: $\qquad \log_{2}2^{5}=5$ $\log_{2}80+\log_{2}x=5$ $\log_{2}(80x)=\log_{2}2^{5}$ ... logarithmic functions are one-to-one, so $ 80x =32\qquad$ ... multiply with $\displaystyle \frac{1}{80}$ $x=\displaystyle \frac{32}{80}=\frac{2}{5}$