Algebra Examples

$\log_{5} (\frac{1}{25}) = - 2$

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, $b = 5$ , $x = \frac{1}{25}$ , and $y = - 2$ .

$b = 5$

$x = \frac{1}{25}$

$y = - 2$

Step 2

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

$5^{- 2} = \frac{1}{25}$