Precalculus Examples

$\log_{3} (x^{2} + 2) - \log_{3} (x - 2) = 2 \log_{3} (x + 2)$

Step 1

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

$\log_{3} (\frac{x^{2} + 2}{x - 2}) = 2 \log_{3} (x + 2)$

Step 2

Simplify $2 \log_{3} (x + 2)$ by moving $2$ inside the logarithm.

$\log_{3} (\frac{x^{2} + 2}{x - 2}) = \log_{3} ({(x + 2)}^{2})$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.4008846$

Step 4