Precalculus Examples

$3 \log_{5} (6 x + 1) + \frac{1}{2} \cdot \log_{5} (x + 5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{5} (6 x + 1)$ by moving $3$ inside the logarithm.

$\log_{5} ({(6 x + 1)}^{3}) + \frac{1}{2} \cdot \log_{5} (x + 5)$

Step 1.2

Simplify $\frac{1}{2} \log_{5} (x + 5)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{5} ({(6 x + 1)}^{3}) + \log_{5} ({(x + 5)}^{\frac{1}{2}})$

Step 2

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

$\log_{5} ({(6 x + 1)}^{3} {(x + 5)}^{\frac{1}{2}})$

Step 3

Reorder factors in $\log_{5} ({(6 x + 1)}^{3} {(x + 5)}^{\frac{1}{2}})$ .

$\log_{5} ({(x + 5)}^{\frac{1}{2}} {(6 x + 1)}^{3})$