Precalculus Examples

$\log_{7} ({(\frac{x^{6}}{x})}^{5})$

Step 1

Expand $\log_{7} ({(\frac{x^{6}}{x})}^{5})$ by moving $5$ outside the logarithm.

$5 \log_{7} (\frac{x^{6}}{x})$

Step 2

Reduce the expression $\frac{x^{6}}{x}$ by cancelling the common factors.

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Step 2.1

Factor $x$ out of $x^{6}$ .

$5 \log_{7} (\frac{x \cdot x^{5}}{x})$

Step 2.2

Raise $x$ to the power of $1$ .

$5 \log_{7} (\frac{x \cdot x^{5}}{x^{1}})$

Step 2.3

Factor $x$ out of $x^{1}$ .

$5 \log_{7} (\frac{x \cdot x^{5}}{x \cdot 1})$

Step 2.4

Cancel the common factor.

$5 \log_{7} (\frac{x \cdot x^{5}}{x \cdot 1})$

Step 2.5

Rewrite the expression.

$5 \log_{7} (\frac{x^{5}}{1})$

Step 3

Divide $x^{5}$ by $1$ .

$5 \log_{7} (x^{5})$

Step 4

Expand $\log_{7} (x^{5})$ by moving $5$ outside the logarithm.

$5 (5 \log_{7} (x))$

Step 5

Multiply $5$ by $5$ .

$25 \log_{7} (x)$