Precalculus Examples

$\frac{\log (3 x)}{\log (3)} = \frac{\log (36)}{\log (3)}$

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, $b = 10$ , $x = 3 x$ , and $y = \frac{\log (36)}{\log (3)}$ .

$b = 10$

$x = 3 x$

$y = \frac{\log (36)}{\log (3)}$

Step 2

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

$10^{\frac{\log (36)}{\log (3)}} = 3 x$