Precalculus Examples

$\frac{1}{2} \cdot \log_{7} (x) + \log_{7} (y) - 4 \log_{7} (x + 5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \log_{7} (x)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{7} (x^{\frac{1}{2}}) + \log_{7} (y) - 4 \log_{7} (x + 5)$

Step 1.2

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

$\log_{7} (x^{\frac{1}{2}}) + \log_{7} (y) - \log_{7} ({(x + 5)}^{4})$

Step 2

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

$\log_{7} (x^{\frac{1}{2}} y) - \log_{7} ({(x + 5)}^{4})$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{7} (\frac{x^{\frac{1}{2}} y}{{(x + 5)}^{4}})$

Step 4

Reorder factors in $\log_{7} (\frac{x^{\frac{1}{2}} y}{{(x + 5)}^{4}})$ .

$\log_{7} (\frac{y x^{\frac{1}{2}}}{{(x + 5)}^{4}})$