Precalculus Examples

$3 \log_{m} (2 w + 1) + \frac{1}{5} \cdot \log_{m} (w + 9)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{m} (2 w + 1)$ by moving $3$ inside the logarithm.

$\log_{m} ({(2 w + 1)}^{3}) + \frac{1}{5} \cdot \log_{m} (w + 9)$

Step 1.2

Simplify $\frac{1}{5} \log_{m} (w + 9)$ by moving $\frac{1}{5}$ inside the logarithm.

$\log_{m} ({(2 w + 1)}^{3}) + \log_{m} ({(w + 9)}^{\frac{1}{5}})$

Step 2

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

$\log_{m} ({(2 w + 1)}^{3} {(w + 9)}^{\frac{1}{5}})$

Step 3

Reorder factors in $\log_{m} ({(2 w + 1)}^{3} {(w + 9)}^{\frac{1}{5}})$ .

$\log_{m} ({(w + 9)}^{\frac{1}{5}} {(2 w + 1)}^{3})$