### Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem8-125

8-125.

Rewrite each expression as a single logarithm.

1. $8\text{log}_{3}\left(y\right) + \text{log}_{3}\left(2x\right)$

The following definitions and properties hold true for all positive numbers, $b,\ m,\text{and } n, \text{and } b\neq$.

 Definition of a log: $\text{log}_{b}(y)=x \text{ means } y=b^{x} \text{ for }y>0$ Product Property: $\text{log}_{b}(m\cdot n)=\text{log}_{b}(m)+\text{log}_{b}(n)$ Quotient Property: $\text{log}_{b}(\frac{m}{n})=\text{log}_{b}(m)-\text{log}_{b}(n)$ Power Property: $\text{log}_{b}(m^n)=n\cdot \text{log}_{b}(m)$

1. $\text{log}_{4}\left(5m\right) - 9\text{log}_{4}\left(n\right)$

$\text{log}_4\left(\frac{5m}{n^9}\right)$