Precalculus Examples

$3 \ln (6) - 4 \ln (x) - 3 \ln (x^{2} + 6)$

Step 1

Simplify each term.

Tap for more steps...

Simplify $3 \ln (6)$ by moving $3$ inside the logarithm.

$\ln (6^{3}) - 4 \ln (x) - 3 \ln (x^{2} + 6)$

Raise $6$ to the power of $3$ .

$\ln (216) - 4 \ln (x) - 3 \ln (x^{2} + 6)$

Simplify $- 4 \ln (x)$ by moving $4$ inside the logarithm.

$\ln (216) - \ln (x^{4}) - 3 \ln (x^{2} + 6)$

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

$\ln (216) - \ln (x^{4}) - \ln ({(x^{2} + 6)}^{3})$

Step 2

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

$\ln (\frac{216}{x^{4}}) - \ln ({(x^{2} + 6)}^{3})$

Step 3

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

$\ln (\frac{\frac{216}{x^{4}}}{{(x^{2} + 6)}^{3}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{216}{x^{4}} \cdot \frac{1}{{(x^{2} + 6)}^{3}})$

Step 5

Combine.

$\ln (\frac{216 \cdot 1}{x^{4} {(x^{2} + 6)}^{3}})$

Step 6

Multiply $216$ by $1$ .

$\ln (\frac{216}{x^{4} {(x^{2} + 6)}^{3}})$