Precalculus Examples

$\log_{8} (3^{x} \cdot 5^{x}) = 0.12$

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, $b = 8$ , $x = 3^{x} \cdot 5^{x}$ , and $y = 0.12$ .

$b = 8$

$x = 3^{x} \cdot 5^{x}$

$y = 0.12$

Step 2

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

$8^{0.12} = 3^{x} \cdot 5^{x}$