Precalculus Examples

$\frac{1}{8} \cdot (5 \ln (x + 4) - \ln (x) - \ln (x^{2} - 25))$

Step 1

Apply the distributive property.

$\frac{1}{8} (5 \ln (x + 4)) + \frac{1}{8} (- \ln (x)) + \frac{1}{8} (- \ln (x^{2} - 25))$

Step 2

Simplify.

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Step 2.1

Multiply $\frac{1}{8} (5 \ln (x + 4))$ .

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Step 2.1.1

Combine $5$ and $\frac{1}{8}$ .

$\frac{5}{8} \ln (x + 4) + \frac{1}{8} (- \ln (x)) + \frac{1}{8} (- \ln (x^{2} - 25))$

Step 2.1.2

Combine $\frac{5}{8}$ and $\ln (x + 4)$ .

$\frac{5 \ln (x + 4)}{8} + \frac{1}{8} (- \ln (x)) + \frac{1}{8} (- \ln (x^{2} - 25))$

Step 2.2

Combine $\frac{1}{8}$ and $\ln (x)$ .

$\frac{5 \ln (x + 4)}{8} - \frac{\ln (x)}{8} + \frac{1}{8} (- \ln (x^{2} - 25))$

Step 2.3

Combine $\frac{1}{8}$ and $\ln (x^{2} - 25)$ .

$\frac{5 \ln (x + 4)}{8} - \frac{\ln (x)}{8} - \frac{\ln (x^{2} - 25)}{8}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 \ln (x + 4) - \ln (x)}{8} - \frac{\ln (x^{2} - 25)}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \ln (x + 4) - \ln (x) - \ln (x^{2} - 25)}{8}$