Precalculus Examples

$\frac{\ln (0.5)}{5730} \cdot 10000$

Step 1

Cancel the common factor of $10$ .

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Step 1.1

Factor $10$ out of $5730$ .

$\frac{\ln (0.5)}{10 (573)} \cdot 10000$

Step 1.2

Factor $10$ out of $10000$ .

$\frac{\ln (0.5)}{10 \cdot 573} \cdot (10 \cdot 1000)$

Step 1.3

Cancel the common factor.

$\frac{\ln (0.5)}{10 \cdot 573} \cdot (10 \cdot 1000)$

Step 1.4

Rewrite the expression.

$\frac{\ln (0.5)}{573} \cdot 1000$

Step 2

Combine $\frac{\ln (0.5)}{573}$ and $1000$ .

$\frac{\ln (0.5) \cdot 1000}{573}$

Step 3

Reorder $\ln (0.5)$ and $1000$ .

$\frac{1000 \cdot \ln (0.5)}{573}$

Step 4

Simplify $1000 \cdot \ln (0.5)$ by moving $1000$ inside the logarithm.

$\frac{\ln ({0.5}^{1000})}{573}$

Step 5

Rewrite $\frac{\ln ({0.5}^{1000})}{573}$ as $\frac{1}{573} \ln ({0.5}^{1000})$ .

$\frac{1}{573} \ln ({0.5}^{1000})$

Step 6

Simplify $\frac{1}{573} \ln ({0.5}^{1000})$ by moving $\frac{1}{573}$ inside the logarithm.

$\ln ({({0.5}^{1000})}^{\frac{1}{573}})$

Step 7

Multiply the exponents in ${({0.5}^{1000})}^{\frac{1}{573}}$ .

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Step 7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln ({0.5}^{1000 (\frac{1}{573})})$

Step 7.2

Combine $1000$ and $\frac{1}{573}$ .

$\ln ({0.5}^{\frac{1000}{573}})$

Step 8

Raise $0.5$ to the power of $\frac{1000}{573}$ .

$\ln (0.29829243)$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\ln (0.29829243)$

Decimal Form:

$- 1.20968094 \dots$