Precalculus Examples

$2 \ln (x) - 3 \ln (x + 7) + \frac{2}{3} \ln (y - 2) - 3$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$\ln (x^{2}) - 3 \ln (x + 7) + \frac{2}{3} \cdot \ln (y - 2) - 3$

Step 1.2

Simplify $- 3 \ln (x + 7)$ by moving $3$ inside the logarithm.

$\ln (x^{2}) - \ln ({(x + 7)}^{3}) + \frac{2}{3} \cdot \ln (y - 2) - 3$

Step 1.3

Simplify $\frac{2}{3} \ln (y - 2)$ by moving $\frac{2}{3}$ inside the logarithm.

$\ln (x^{2}) - \ln ({(x + 7)}^{3}) + \ln ({(y - 2)}^{\frac{2}{3}}) - 3$

Step 2

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

$\ln (\frac{x^{2}}{{(x + 7)}^{3}}) + \ln ({(y - 2)}^{\frac{2}{3}}) - 3$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (\frac{x^{2}}{{(x + 7)}^{3}} {(y - 2)}^{\frac{2}{3}}) - 3$

Step 4

Combine $\frac{x^{2}}{{(x + 7)}^{3}}$ and ${(y - 2)}^{\frac{2}{3}}$ .

$\ln (\frac{x^{2} {(y - 2)}^{\frac{2}{3}}}{{(x + 7)}^{3}}) - 3$