Precalculus Examples

$\ln (x^{5}) \cdot (5 \ln (x))$

Step 1

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

$5 \ln (x) \cdot (5 \ln (x))$

Step 2

Multiply $5 \ln (x) (5 \ln (x))$ .

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Step 2.1

Multiply $5$ by $5$ .

$25 \ln (x) \ln (x)$

Step 2.2

Raise $\ln (x)$ to the power of $1$ .

$25 (\ln^{1} (x) \ln (x))$

Step 2.3

Raise $\ln (x)$ to the power of $1$ .

$25 (\ln^{1} (x) \ln^{1} (x))$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 {\ln (x)}^{1 + 1}$

Step 2.5

Add $1$ and $1$ .

$25 \ln^{2} (x)$