Precalculus Examples

$5 \log_{7} (6 y + 1) + \frac{1}{5 \log_{7} (y + 5)}$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{7} (6 y + 1)$ by moving $5$ inside the logarithm.

$\log_{7} ({(6 y + 1)}^{5}) + \frac{1}{5 \log_{7} (y + 5)}$

Step 1.2

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

$\log_{7} ({(6 y + 1)}^{5}) + \frac{1}{\log_{7} ({(y + 5)}^{5})}$

Step 2

To write $\log_{7} ({(6 y + 1)}^{5})$ as a fraction with a common denominator, multiply by $\frac{\log_{7} ({(y + 5)}^{5})}{\log_{7} ({(y + 5)}^{5})}$ .

$\frac{\log_{7} ({(6 y + 1)}^{5}) \log_{7} ({(y + 5)}^{5})}{\log_{7} ({(y + 5)}^{5})} + \frac{1}{\log_{7} ({(y + 5)}^{5})}$

Step 3

Combine the numerators over the common denominator.

$\frac{\log_{7} ({(6 y + 1)}^{5}) \log_{7} ({(y + 5)}^{5}) + 1}{\log_{7} ({(y + 5)}^{5})}$