Precalculus Examples

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

Step 1

Simplify $5 \ln (x^{2} + 4 x)$ by moving $5$ inside the logarithm.

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

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 3

Apply the distributive property.

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

Step 4

Simplify $\frac{1}{2} \ln (x {(x^{2} + 4 x)}^{5} - 4 {(x^{2} + 4 x)}^{5})$ by moving $\frac{1}{2}$ inside the logarithm.

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