Precalculus Examples

$\log_{5} (3 x - 1) = 3$

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, $b = 5$ , $x = 3 x - 1$ , and $y = 3$ .

$b = 5$

$x = 3 x - 1$

$y = 3$

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

$5^{3} = 3 x - 1$