Answer
See explanation
Work Step by Step
Recall that:
$$\log_{b}x=\frac{\ln(x)}{\ln(b)}$$
Multiply the numerator and the denominator by $\frac{1}{\ln(a)}$:
$$\log_{b}x=\frac{\ln(x)\cdot \frac{1}{\ln(a)}}{\ln(b)\cdot \frac{1}{\ln(a)}}$$ where $a\neq 1$ and $b \neq 1$ and $a \gt 0$ and $b \gt 0$.
$$\log_{b}x=\frac{\frac{\ln(x)}{\ln(a)}}{\frac{\ln(b)}{\ln(a)}}$$
$$\log_{b}x=\frac{\log_{a}x}{\log_{a}b}$$
where $a\neq 1$ and $b \neq 1$ and $a \gt 0$ and $b \gt 0$.
