Precalculus Examples

$- 0.25 \ln (1 - \frac{1}{2} \cdot 0.1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Cancel the common factor of $0.1$ .

Tap for more steps...

Step 1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 0.25 \ln (1 + \frac{- 1}{2} \cdot 0.1)$

Step 1.1.2

Factor $0.1$ out of $2$ .

$- 0.25 \ln (1 + \frac{- 1}{0.1 (20)} \cdot 0.1)$

Step 1.1.3

Cancel the common factor.

$- 0.25 \ln (1 + \frac{- 1}{0.1 \cdot 20} \cdot 0.1)$

Step 1.1.4

Rewrite the expression.

$- 0.25 \ln (1 + \frac{- 1}{20})$

Step 1.2

Move the negative in front of the fraction.

$- 0.25 \ln (1 - \frac{1}{20})$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

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

$- 0.25 \ln (\frac{20}{20} - \frac{1}{20})$

Step 2.2

Combine the numerators over the common denominator.

$- 0.25 \ln (\frac{20 - 1}{20})$

Step 2.3

Subtract $1$ from $20$ .

$- 0.25 \ln (\frac{19}{20})$

Step 3

Simplify $- 0.25 \ln (\frac{19}{20})$ by moving $0.25$ inside the logarithm.

$- \ln ({(\frac{19}{20})}^{0.25})$

Step 4

Apply the product rule to $\frac{19}{20}$ .

$- \ln (\frac{19^{0.25}}{20^{0.25}})$

Step 5

Raise $19$ to the power of $0.25$ .

$- \ln (\frac{2.08779762}{20^{0.25}})$

Step 6

Raise $20$ to the power of $0.25$ .

$- \ln (\frac{2.08779762}{2.11474252})$

Step 7

Divide $2.08779762$ by $2.11474252$ .

$- \ln (0.98725854)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \ln (0.98725854)$

Decimal Form:

$0.01282332 \dots$