Precalculus Examples

$70 e^{(\frac{1}{1690} \cdot \ln (\frac{1}{2})) (220)}$

Step 1

Rewrite $\ln (\frac{1}{2})$ as $\ln (1) - \ln (2)$ .

$70 e^{\frac{1}{1690} \cdot (\ln (1) - \ln (2)) \cdot 220}$

Step 2

The natural logarithm of $1$ is $0$ .

$70 e^{\frac{1}{1690} \cdot (0 - \ln (2)) \cdot 220}$

Step 3

Subtract $\ln (2)$ from $0$ .

$70 e^{\frac{1}{1690} \cdot (- \ln (2)) \cdot 220}$

Step 4

Combine $\frac{1}{1690}$ and $\ln (2)$ .

$70 e^{- \frac{\ln (2)}{1690} \cdot 220}$

Step 5

Cancel the common factor of $10$ .

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Step 5.1

Move the leading negative in $- \frac{\ln (2)}{1690}$ into the numerator.

$70 e^{\frac{- \ln (2)}{1690} \cdot 220}$

Step 5.2

Factor $10$ out of $1690$ .

$70 e^{\frac{- \ln (2)}{10 (169)} \cdot 220}$

Step 5.3

Factor $10$ out of $220$ .

$70 e^{\frac{- \ln (2)}{10 \cdot 169} \cdot (10 \cdot 22)}$

Step 5.4

Cancel the common factor.

$70 e^{\frac{- \ln (2)}{10 \cdot 169} \cdot (10 \cdot 22)}$

Step 5.5

Rewrite the expression.

$70 e^{\frac{- \ln (2)}{169} \cdot 22}$

Step 6

Combine $\frac{- \ln (2)}{169}$ and $22$ .

$70 e^{\frac{- \ln (2) \cdot 22}{169}}$

Step 7

Multiply $22$ by $- 1$ .

$70 e^{\frac{- 22 \ln (2)}{169}}$

Step 8

Move the negative in front of the fraction.

$70 e^{- \frac{22 \ln (2)}{169}}$