### Home > INT3 > Chapter 8 > Lesson 8.1.1 > Problem8-17

8-17.

Given that $\text{log}\left(2\right) ≈ 0.3010, \text{log}\left(3\right) ≈ 0.4771$, and $\text{log}\left(5\right) ≈ 0.6990$, calculate each of the following logarithms without using the log button on your calculator.

1. $\text{log}(6)$

$\text{log}\left(6\right) = \text{log} \left(2 · 3\right)$
Now use the properties of logarithms to expand.

$\text{log} \left(2\right) + \text{log} \left(3\right) ≈ 0.7781$

1. $\text{log}(15)$

Express $15$ as a product of numbers whose logs are given. Then see the step in part (a).

1. $\text{log}(9)$

$\text{log}\left(9\right)$ can be rewritten as $\text{log}\left(3 · 3\right)$ or $\text{log}\left(3^{2}\right)$. Try both.

1. $\text{log}(50)$

$50 = 2 · 5^{2}$