Precalculus Examples

$3 \log_{7} (5) + (4 \log_{7} (y - 6) - 5 \log_{7} (y))$

Step 1

Remove parentheses.

$3 \log_{7} (5) + 4 \log_{7} (y - 6) - 5 \log_{7} (y)$

Step 2

Simplify each term.

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Step 2.1

Simplify $3 \log_{7} (5)$ by moving $3$ inside the logarithm.

$\log_{7} (5^{3}) + 4 \log_{7} (y - 6) - 5 \log_{7} (y)$

Step 2.2

Raise $5$ to the power of $3$ .

$\log_{7} (125) + 4 \log_{7} (y - 6) - 5 \log_{7} (y)$

Step 2.3

Simplify $4 \log_{7} (y - 6)$ by moving $4$ inside the logarithm.

$\log_{7} (125) + \log_{7} ({(y - 6)}^{4}) - 5 \log_{7} (y)$

Step 2.4

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

$\log_{7} (125) + \log_{7} ({(y - 6)}^{4}) - \log_{7} (y^{5})$

Step 3

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

$\log_{7} (125 {(y - 6)}^{4}) - \log_{7} (y^{5})$

Step 4

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

$\log_{7} (\frac{125 {(y - 6)}^{4}}{y^{5}})$