Precalculus Examples

$\log (4^{5 x}) = \log (16^{2 x - 1})$

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, $b = 10$ , $x = 4^{5 x}$ , and $y = \log (16^{2 x - 1})$ .

$b = 10$

$x = 4^{5 x}$

$y = \log (16^{2 x - 1})$

Step 2

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

$10^{\log (16^{2 x - 1})} = 4^{5 x}$