Precalculus Examples

$4 \log_{5} (7 x + 1) + 0.5 \log_{5} (x + 3)$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \log_{5} (7 x + 1)$ by moving $4$ inside the logarithm.

$\log_{5} ({(7 x + 1)}^{4}) + 0.5 \log_{5} (x + 3)$

Step 1.2

Simplify $0.5 \log_{5} (x + 3)$ by moving $0.5$ inside the logarithm.

$\log_{5} ({(7 x + 1)}^{4}) + \log_{5} ({(x + 3)}^{0.5})$

Step 2

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

$\log_{5} ({(7 x + 1)}^{4} {(x + 3)}^{0.5})$

Step 3

Reorder factors in $\log_{5} ({(7 x + 1)}^{4} {(x + 3)}^{0.5})$ .

$\log_{5} ({(x + 3)}^{0.5} {(7 x + 1)}^{4})$