Answer
-1.29
Work Step by Step
We are given that $log_{b}2=.43$ and that $ log_{b}3=.68$.
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, $log_{b}\frac{4}{32}= log_{b}4-log_{b}32= log_{b}2^{2}-log_{b}2^{5}$
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).
$log_{b}2^{2}-log_{b}2^{5}=2log_{b}2-5log_{b}2=-3log_{b}2=-3\times.43=-1.29$.
