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

7-26.
1. How do ratios of logs in different bases compare? Homework Help ✎

1. What is ?

2. What is ?

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 log2(7) into a logarithmic expression using a base of 5.

Use your calculator to evaluate this expression.

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

log27 = x
2x = 7

Take the log base 5 of both sides.
log5(2x) = log57

Use the Power Property of Logarithms.
x(log52) = log57

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

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