Calculus Examples

$\frac{\ln (4)}{8} = r$

Step 1

Rewrite the equation as $r = \frac{\ln (4)}{8}$ .

$r = \frac{\ln (4)}{8}$

Step 2

Simplify $\frac{\ln (4)}{8}$ .

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Step 2.1

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

$r = \frac{\ln (2^{2})}{8}$

Step 2.2

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

$r = \frac{2 \ln (2)}{8}$

Step 2.3

Cancel the common factor of $2$ and $8$ .

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Step 2.3.1

Factor $2$ out of $2 \ln (2)$ .

$r = \frac{2 (\ln (2))}{8}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $8$ .

$r = \frac{2 \ln (2)}{2 \cdot 4}$

Step 2.3.2.2

Cancel the common factor.

$r = \frac{2 \ln (2)}{2 \cdot 4}$

Step 2.3.2.3

Rewrite the expression.

$r = \frac{\ln (2)}{4}$

Step 2.4

Rewrite $\frac{\ln (2)}{4}$ as $\frac{1}{4} \ln (2)$ .

$r = \frac{1}{4} \ln (2)$

Step 2.5

Simplify $\frac{1}{4} \ln (2)$ by moving $\frac{1}{4}$ inside the logarithm.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$r = 0.17328679 \dots$