Precalculus Examples

$3 \log (x) = 2$

Divide both sides by $3$ to remove it from the front of the logarithm.

$\frac{3 \log (x)}{3} = \frac{2}{3}$

Simplify each side of the equation.

$\log (x) = \frac{2}{3}$

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, $b = 10$ , $x = x$ , and $y = \frac{2}{3}$ .

$b = 10$

$x = x$

$y = \frac{2}{3}$

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

$10^{\frac{2}{3}} = x$