Precalculus Examples

$\log_{\sqrt{3}} (27) = 6$

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, $b = \sqrt{3}$ , $x = 27$ , and $y = 6$ .

$b = \sqrt{3}$

$x = 27$

$y = 6$

Step 2

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

${\sqrt{3}}^{6} = 27$