CPM Homework Help : INT3 Problem 7-24

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7-24.

Rewrite each equation as an equivalent equation using log base $10$ . You do not need to calculate a numerical answer. These are sometimes known as change of base problems.

$\text{log}_{2}\left(3\right) = x$
Step 1(a):
Write the equation in exponential form.
$2^{x} = 3$
Step 2(a):
Take the logarithm of base $10$ .
$\text{log}_{10}\left(2^{x}\right) = \text{log}_{10}\left(3\right)$
Step 3(a):
Use the Power Property of Logarithms and solve for $x$ .
$x\text{log}_{10}\left(2\right) = \text{log}_{10}\left(3\right)$
Answer (a):
$x= \frac{ \log_{10}(3) }{\log_{10}(2) }$

$\text{log}_{5}\left(8\right) = x$
Hint (b):
Use the same process as in part (a).
Answer (b):
$x= \frac{ \log_{10}(8) }{ \log_{10}(5)}$

$\text{log}_{7}\left(12\right) = x$
Hint (c):
Use the same process as in part (a).

$\text{log}_{a}\left(b\right) = x$
Hint (d):
Use the same process as in part (a).

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