Precalculus Examples

$\log_{\frac{1}{4}} (16) = - 2$

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, $b = \frac{1}{4}$ , $x = 16$ , and $y = - 2$ .

$b = \frac{1}{4}$

$x = 16$

$y = - 2$

Step 2

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

${(\frac{1}{4})}^{- 2} = 16$