Precalculus Examples

$\frac{1}{2} \cdot \ln ({(8)}^{2})$

Step 1

Raise $8$ to the power of $2$ .

$\frac{1}{2} \cdot \ln (64)$

Step 2

Simplify $\frac{1}{2} \ln (64)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (64^{\frac{1}{2}})$

Step 3

Simplify the expression.

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Step 3.1

Rewrite $64$ as $8^{2}$ .

$\ln ({(8^{2})}^{\frac{1}{2}})$

Step 3.2

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

$\ln (8^{2 (\frac{1}{2})})$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$\ln (8^{2 (\frac{1}{2})})$

Step 4.2

Rewrite the expression.

$\ln (8^{1})$

Step 5

Evaluate the exponent.

$\ln (8)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\ln (8)$

Decimal Form:

$2.07944154 \dots$