### Home > INT3 > Chapter 7 > Lesson 7.1.2 > Problem7-26

7-26.

How do ratios of logs in different bases compare? Homework Help ✎

1. What is $\frac { \operatorname { log } _ { 2 } 32 } { \operatorname { log } _ { 2 } 4 }$?

Use your calculator to evaluate this expression.

$\frac{5}{2} \text{ or }\ 2.5$

2. What is $\frac { \operatorname { log } 32 } { \operatorname { log } 4 }$?

3. What do you notice about your answers for parts (a) and (b)? Use the change of base formula to explain your results.

4. Change $\text{log}_{2}\left(7\right)$ into a logarithmic expression using a base of $5$.

Start with the definition of the logarithm.
$\text{log}_{2}7 = x$
$2^{x} = 7$

Take the log base $5$ of both sides.
$\text{log}_{5}(2x) = \text{log}_{5}7$

Use the Power Property of Logarithms.
$x\left(\text{log}_{5}2\right) = \text{log}_{5}7$

$\log_{2}7 =\frac{\log_{5}7}{\log_{5}2}$

Notice that this answer shows a very quick way to change bases.