Precalculus Examples

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

Step 1

Simplify $2 \ln (x + 3)$ by moving $2$ inside the logarithm.

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $\frac{1}{3} (\ln ({(x + 3)}^{2}) \ln (x))$ .

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Step 3.1

Reorder $\ln ({(x + 3)}^{2})$ and $\frac{1}{3}$ .

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

Step 3.2

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

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

Step 4

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

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

Step 5

Multiply the exponents in ${({(x + 3)}^{2})}^{\frac{1}{3}}$ .

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Step 5.1

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

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

Step 5.2

Combine $2$ and $\frac{1}{3}$ .

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