Precalculus Examples

$\frac{\ln (0.2)}{- 9.4 \cdot 10^{- 5}}$

Step 1

Simplify the expression.

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Step 1.1

Move $10^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\ln (0.2) \cdot 10^{5}}{- 9.4}$

Step 1.2

Raise $10$ to the power of $5$ .

$\frac{\ln (0.2) \cdot 100000}{- 9.4}$

Step 2

Simplify the numerator.

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Step 2.1

Reorder $\ln (0.2)$ and $100000$ .

$\frac{100000 \cdot \ln (0.2)}{- 9.4}$

Step 2.2

Simplify $100000 \cdot \ln (0.2)$ by moving $100000$ inside the logarithm.

$\frac{\ln ({0.2}^{100000})}{- 9.4}$

Step 3

Move the negative in front of the fraction.

$- \frac{\ln ({0.2}^{100000})}{9.4}$

Step 4

Replace $e$ with an approximation.

$- \frac{\log_{2.71828182} ({0.2}^{100000})}{9.4}$

Step 5

Expand $\log_{2.71828182} ({0.2}^{100000})$ by moving $100000$ outside the logarithm.

$- \frac{100000 \log_{2.71828182} (0.2)}{9.4}$

Step 6

Log base $2.71828182$ of $0.2$ is approximately $- 1.60943791$ .

$- \frac{100000 \cdot - 1.60943791}{9.4}$

Step 7

Multiply $100000$ by $- 1.60943791$ .

$- \frac{- 160943.79124341}{9.4}$

Step 8

Divide $- 160943.79124341$ by $9.4$ .

$- - 17121.67991951$

Step 9

Multiply $- 1$ by $- 17121.67991951$ .

$17121.67991951$