Precalculus Examples

$- \frac{5}{13} \cdot \ln (1 - \frac{13 \cdot 2}{60})$

Step 1

Cancel the common factor of $2$ and $60$ .

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Step 1.1

Factor $2$ out of $13 \cdot 2$ .

$- \frac{5}{13} \cdot \ln (1 - \frac{2 \cdot 13}{60})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $60$ .

$- \frac{5}{13} \cdot \ln (1 - \frac{2 \cdot 13}{2 \cdot 30})$

Step 1.2.2

Cancel the common factor.

$- \frac{5}{13} \cdot \ln (1 - \frac{2 \cdot 13}{2 \cdot 30})$

Step 1.2.3

Rewrite the expression.

$- \frac{5}{13} \cdot \ln (1 - \frac{13}{30})$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$- \frac{5}{13} \cdot \ln (\frac{30}{30} - \frac{13}{30})$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{5}{13} \cdot \ln (\frac{30 - 13}{30})$

Step 2.3

Subtract $13$ from $30$ .

$- \frac{5}{13} \cdot \ln (\frac{17}{30})$

Step 3

Multiply $- \frac{5}{13} \ln (\frac{17}{30})$ .

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Step 3.1

Reorder $\ln (\frac{17}{30})$ and $\frac{5}{13}$ .

$- (\frac{5}{13} \ln (\frac{17}{30}))$

Step 3.2

Simplify $\frac{5}{13} \ln (\frac{17}{30})$ by moving $\frac{5}{13}$ inside the logarithm.

$- \ln ({(\frac{17}{30})}^{\frac{5}{13}})$

Step 4

Apply the product rule to $\frac{17}{30}$ .

$- \ln (\frac{17^{\frac{5}{13}}}{30^{\frac{5}{13}}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \ln (\frac{17^{\frac{5}{13}}}{30^{\frac{5}{13}}})$

Decimal Form:

$0.21845539 \dots$