Precalculus Examples

$\frac{\log_{2} (8)}{\log_{2} (32)} = x$

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, $b = 2$ , $x = 8$ , and $y = x$ .

$b = 2$

$x = 8$

$y = x$

Step 2

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

$2^{x} = 8$