Precalculus Examples

$x = \log_{5} (\frac{1}{125})$

Step 1

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 5$ , $x = \frac{1}{125}$ , and $y = x$ .

$b = 5$

$x = \frac{1}{125}$

$y = x$

Step 2

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$5^{x} = \frac{1}{125}$