Precalculus Examples

$\log_{x} (6) = \frac{1}{2}$

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, $b = x$ , $x = 6$ , and $y = \frac{1}{2}$ .

$b = x$

$x = 6$

$y = \frac{1}{2}$

Step 2

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

$x^{\frac{1}{2}} = 6$