Precalculus Examples

$\frac{1}{5} \cdot \ln (2 + \frac{1}{2})$

Step 1

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{5} \cdot \ln (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2

Combine $2$ and $\frac{2}{2}$ .

$\frac{1}{5} \cdot \ln (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 3

Combine the numerators over the common denominator.

$\frac{1}{5} \cdot \ln (\frac{2 \cdot 2 + 1}{2})$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $2$ .

$\frac{1}{5} \cdot \ln (\frac{4 + 1}{2})$

Step 4.2

Add $4$ and $1$ .

$\frac{1}{5} \cdot \ln (\frac{5}{2})$

Step 5

Simplify $\frac{1}{5} \ln (\frac{5}{2})$ by moving $\frac{1}{5}$ inside the logarithm.

$\ln ({(\frac{5}{2})}^{\frac{1}{5}})$

Step 6

Apply the product rule to $\frac{5}{2}$ .

$\ln (\frac{5^{\frac{1}{5}}}{2^{\frac{1}{5}}})$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{5^{\frac{1}{5}}}{2^{\frac{1}{5}}})$

Decimal Form:

$0.18325814 \dots$