Precalculus Examples

$\ln (x + \frac{1}{2}) \ln (x - 1) - \frac{1}{3} \cdot \ln (x + 7) - 5 \ln (2 x + 5)$

Step 1

Multiply $- \frac{1}{3} \ln (x + 7)$ .

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Step 1.1

Reorder $\ln (x + 7)$ and $\frac{1}{3}$ .

$\ln (x + \frac{1}{2}) \ln (x - 1) - (\frac{1}{3} \ln (x + 7)) - 5 \ln (2 x + 5)$

Step 1.2

Simplify $\frac{1}{3} \ln (x + 7)$ by moving $\frac{1}{3}$ inside the logarithm.

$\ln (x + \frac{1}{2}) \ln (x - 1) - \ln ({(x + 7)}^{\frac{1}{3}}) - 5 \ln (2 x + 5)$

Step 2

Simplify $- 5 \ln (2 x + 5)$ by moving $5$ inside the logarithm.

$\ln (x + \frac{1}{2}) \ln (x - 1) - \ln ({(x + 7)}^{\frac{1}{3}}) - \ln ({(2 x + 5)}^{5})$