Precalculus Examples

$\frac{1}{3} \cdot (5 \ln (x + 6) - \ln (x - \ln (x^{2}) - 25))$

Step 1

Simplify $5 \ln (x + 6)$ by moving $5$ inside the logarithm.

$\frac{1}{3} \cdot (\ln ({(x + 6)}^{5}) - \ln (x - \ln (x^{2}) - 25))$

Step 2

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

$\frac{1}{3} \cdot \ln (\frac{{(x + 6)}^{5}}{x - \ln (x^{2}) - 25})$

Step 3

Simplify $\frac{1}{3} \ln (\frac{{(x + 6)}^{5}}{x - \ln (x^{2}) - 25})$ by moving $\frac{1}{3}$ inside the logarithm.

$\ln ({(\frac{{(x + 6)}^{5}}{x - \ln (x^{2}) - 25})}^{\frac{1}{3}})$

Step 4

Apply the product rule to $\frac{{(x + 6)}^{5}}{x - \ln (x^{2}) - 25}$ .

$\ln (\frac{{({(x + 6)}^{5})}^{\frac{1}{3}}}{{(x - \ln (x^{2}) - 25)}^{\frac{1}{3}}})$

Step 5

Multiply the exponents in ${({(x + 6)}^{5})}^{\frac{1}{3}}$ .

Tap for more steps...

Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln (\frac{{(x + 6)}^{5 (\frac{1}{3})}}{{(x - \ln (x^{2}) - 25)}^{\frac{1}{3}}})$

Step 5.2

Combine $5$ and $\frac{1}{3}$ .

$\ln (\frac{{(x + 6)}^{\frac{5}{3}}}{{(x - \ln (x^{2}) - 25)}^{\frac{1}{3}}})$