Precalculus Examples

$\frac{1}{3} \cdot \log_{8} (x + 2) + 7 \log_{8} (x)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{3} \log_{8} (x + 2)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{8} ({(x + 2)}^{\frac{1}{3}}) + 7 \log_{8} (x)$

Step 1.2

Simplify $7 \log_{8} (x)$ by moving $7$ inside the logarithm.

$\log_{8} ({(x + 2)}^{\frac{1}{3}}) + \log_{8} (x^{7})$

Step 2

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

$\log_{8} ({(x + 2)}^{\frac{1}{3}} x^{7})$

Step 3

Reorder factors in $\log_{8} ({(x + 2)}^{\frac{1}{3}} x^{7})$ .

$\log_{8} (x^{7} {(x + 2)}^{\frac{1}{3}})$