Precalculus Examples

$\log (x) = 2 \log (a) - \log (b)$

Step 1

Simplify the right side.

Tap for more steps...

Step 1.1

Simplify $2 \log (a) - \log (b)$ .

Tap for more steps...

Step 1.1.1

Simplify $2 \log (a)$ by moving $2$ inside the logarithm.

$\log (x) = \log (a^{2}) - \log (b)$

Step 1.1.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (x) = \log (\frac{a^{2}}{b})$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x = \frac{a^{2}}{b}$