### Home > AC > Chapter 13 > Lesson 13.OF1-S > Problem7-129

7-129.

Write three different, but equivalent, expressions for each of the following logs. For example: $\log(7^{3/2})$ can be written as $\frac{3}{2}\log(7)$, $\frac{1}{2}\log(7^3)$$3\log\left(\sqrt{7}\right)$, etc. .

Use the properties of logarithms and exponents to help you rewrite these.
Simplify different parts of the expression to create new, equivalent expressions.

1. $\log(8^{2/3})$

Simplify the argument:

Simplify the argument further:

The Power Property of Logarithms is $\log_m(a^n)=n\cdot\log m(a)$, so one way to rewrite this expression is $\frac{2}{3}\log(8)$.

2. $−2\log(5)$

Use the Power Property of Logarithms in reverse here.
Since $n·\log_m(a)=\log_m(a^n),−2\log(5)=\log(5^{−2})$.

Find two different ways to rewrite $5^{−2}$
(there are more than two ways to do this).

3. $\log(na)^{bo}$

Refer to parts (a) and (b).