Home > INT3 > Chapter 7 > Lesson 7.1.2 > Problem7-24

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.

1. $\text{log}_{2}\left(3\right) = x$

Write the equation in exponential form.

$2^{x} = 3$

Take the logarithm of base $10$.

$\text{log}_{10}\left(2^{x}\right) = \text{log}_{10}\left(3\right)$

Use the Power Property of Logarithms and solve for $x$.

$x\text{log}_{10}\left(2\right) = \text{log}_{10}\left(3\right)$

$x= \frac{ \log_{10}(3) }{\log_{10}(2) }$

1. $\text{log}_{5}\left(8\right) = x$

Use the same process as in part (a).

$x= \frac{ \log_{10}(8) }{ \log_{10}(5)}$

1. $\text{log}_{7}\left(12\right) = x$

Use the same process as in part (a).

1. $\text{log}_{a}\left(b\right) = x$

Use the same process as in part (a).