Precalculus Examples

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

Step 1

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

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

Step 2

Add $2$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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