Precalculus Examples

$\frac{1}{2} \cdot (\frac{\log_{7} (a b)}{5 \log_{7} (c)})$

Step 1

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

$\frac{1}{2} \cdot \frac{\log_{7} (a b)}{\log_{7} (c^{5})}$

Step 2

Combine.

$\frac{1 \log_{7} (a b)}{2 \log_{7} (c^{5})}$

Step 3

Multiply $\log_{7} (a b)$ by $1$ .

$\frac{\log_{7} (a b)}{2 \log_{7} (c^{5})}$

Step 4

Simplify $2 \log_{7} (c^{5})$ by moving $2$ inside the logarithm.

$\frac{\log_{7} (a b)}{\log_{7} ({(c^{5})}^{2})}$

Step 5

Multiply the exponents in ${(c^{5})}^{2}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\log_{7} (a b)}{\log_{7} (c^{5 \cdot 2})}$

Step 5.2

Multiply $5$ by $2$ .

$\frac{\log_{7} (a b)}{\log_{7} (c^{10})}$