Precalculus Examples

$\frac{6 \ln ({(4)}^{5})}{4}$

Step 1

Expand $\ln ({(4)}^{5})$ by moving $5$ outside the logarithm.

$\frac{6 (5 \ln (4))}{4}$

Step 2

Cancel the common factor of $6$ and $4$ .

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Step 2.1

Factor $2$ out of $6 (5 \ln (4))$ .

$\frac{2 (3 (5 \ln (4)))}{4}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $4$ .

$\frac{2 (3 (5 \ln (4)))}{2 (2)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (3 (5 \ln (4)))}{2 \cdot 2}$

Step 2.2.3

Rewrite the expression.

$\frac{3 (5 \ln (4))}{2}$

Step 3

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\frac{3 (5 \ln (2^{2}))}{2}$

Step 4

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{3 (5 (2 \ln (2)))}{2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$\frac{3 (5 (2 \ln (2)))}{2}$

Step 5.2

Divide $3 (5 (\ln (2)))$ by $1$ .

$3 (5 (\ln (2)))$

Step 6

Simplify $5 (\ln (2))$ by moving $5$ inside the logarithm.

$3 \ln (2^{5})$

Step 7

Raise $2$ to the power of $5$ .

$3 \ln (32)$

Step 8

Simplify $3 \ln (32)$ by moving $3$ inside the logarithm.

$\ln (32^{3})$

Step 9

Raise $32$ to the power of $3$ .

$\ln (32768)$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\ln (32768)$

Decimal Form:

$10.39720770 \dots$