Precalculus Examples

$\log_{6} (5 x^{2}) = 2 \log_{6} (5 x)$

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, $b = 6$ , $x = 5 x^{2}$ , and $y = 2 \log_{6} (5 x)$ .

$b = 6$

$x = 5 x^{2}$

$y = 2 \log_{6} (5 x)$

Step 2

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

$6^{2 \log_{6} (5 x)} = 5 x^{2}$