Answer
-.09
Work Step by Step
We are given that $log_{b}2=.36$ and that $ log_{b}5=.83$.
The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{b}\frac{4}{5}= log_{b}\frac{2^{2}}{5}=log_{b}2^{2}-log_{b}5$.
The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number).
Therefore, $log_{b}2^{2}-log_{b}5=2log_{b}2-log_{b}5=2\times.36-.83=-.09$
