Precalculus Examples

$\log_{3} (3^{5 x + 1}) = 2$

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, $b = 3$ , $x = 3^{5 x + 1}$ , and $y = 2$ .

$b = 3$

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

$y = 2$

Step 2

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

$3^{2} = 3^{5 x + 1}$