Answer
2.02
Work Step by Step
We are given that $log_{b}2=.36$ and that $ log_{b}5=.83$.
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{b}50= .log_{b}(2\times25)=.log_{b}(2\times5^{2})=log_{b}2+log_{b}5^{2}$.
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, $log_{b}2+log_{b}5^{2}=log_{b}2+2log_{b}5=.36+2(.83)=2.02$
