Calculus Examples

$\frac{1}{2} \cdot \ln (16)$

Step 1

Simplify $\frac{1}{2} \ln (16)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (16^{\frac{1}{2}})$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\ln ({(4^{2})}^{\frac{1}{2}})$

Step 2.2

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

$\ln (4^{2 (\frac{1}{2})})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$\ln (4^{2 (\frac{1}{2})})$

Step 3.2

Rewrite the expression.

$\ln (4^{1})$

Step 4

Evaluate the exponent.

$\ln (4)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (4)$

Decimal Form:

$1.38629436 \dots$