Precalculus Examples

$\log_{x} (6^{13}) = 26$

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, $b = x$ , $x = 6^{13}$ , and $y = 26$ .

$b = x$

$x = 6^{13}$

$y = 26$

Step 2

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

$x^{26} = 6^{13}$