Precalculus Examples

$\frac{0.3 (e) (\ln (\frac{0.27}{0.3}))}{30} \cdot 180$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $0.3$ by $e$ .

$\frac{0.81548454 \ln (\frac{0.27}{0.3})}{30} \cdot 180$

Step 1.2

Simplify $0.81548454 \ln (\frac{0.27}{0.3})$ by moving $0.81548454$ inside the logarithm.

$\frac{\ln ({(\frac{0.27}{0.3})}^{0.81548454})}{30} \cdot 180$

Step 2

Simplify the numerator.

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Step 2.1

Divide $0.27$ by $0.3$ .

$\frac{\ln ({0.9}^{0.81548454})}{30} \cdot 180$

Step 2.2

Raise $0.9$ to the power of $0.81548454$ .

$\frac{\ln (0.91766775)}{30} \cdot 180$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $30$ .

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Step 3.1.1

Factor $30$ out of $180$ .

$\frac{\ln (0.91766775)}{30} \cdot (30 (6))$

Step 3.1.2

Cancel the common factor.

$\frac{\ln (0.91766775)}{30} \cdot (30 \cdot 6)$

Step 3.1.3

Rewrite the expression.

$\ln (0.91766775) \cdot 6$

Step 3.2

Reorder $\ln (0.91766775)$ and $6$ .

$6 \cdot \ln (0.91766775)$

Step 4

Simplify $6 \cdot \ln (0.91766775)$ by moving $6$ inside the logarithm.

$\ln ({0.91766775}^{6})$

Step 5

Raise $0.91766775$ to the power of $6$ .

$\ln (0.59719043)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\ln (0.59719043)$

Decimal Form:

$- 0.51551923 \dots$