Precalculus Examples

$\log_{b} (x y) = (\log_{b} (x)) (\log_{b} (y))$

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, $b = b$ , $x = x y$ , and $y = (\log_{b} (x)) (\log_{b} (y))$ .

$b = b$

$x = x y$

$y = (\log_{b} (x)) (\log_{b} (y))$

Step 2

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

$b^{(\log_{b} (x)) (\log_{b} (y))} = x y$