CPM Homework Help : INT3 Problem 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.

$\text{log}(6)$
Step (a):
$\text{log}\left(6\right) = \text{log} \left(2 · 3\right)$
Now use the properties of logarithms to expand.
Answer (a):
$\text{log} \left(2\right) + \text{log} \left(3\right) ≈ 0.7781$

$\text{log}(15)$
Hint (b):
Express $15$ as a product of numbers whose logs are given. Then see the step in part (a).

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

$\text{log}(50)$
Hint (d):
$50 = 2 · 5^{2}$