Precalculus Examples

$3 e^{- (- \frac{\ln (\frac{1}{2})}{5715} \cdot 1000)}$

Step 1

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

$3 e^{- (- \frac{\ln (1) - \ln (2)}{5715} \cdot 1000)}$

Step 2

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

$3 e^{- (- \frac{0 - \ln (2)}{5715} \cdot 1000)}$

Step 3

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

$3 e^{- (- \frac{- \ln (2)}{5715} \cdot 1000)}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Move the leading negative in $- \frac{- \ln (2)}{5715}$ into the numerator.

$3 e^{- (\frac{\ln (2)}{5715} \cdot 1000)}$

Step 4.2

Factor $5$ out of $5715$ .

$3 e^{- (\frac{\ln (2)}{5 (1143)} \cdot 1000)}$

Step 4.3

Factor $5$ out of $1000$ .

$3 e^{- (\frac{\ln (2)}{5 \cdot 1143} \cdot (5 \cdot 200))}$

Step 4.4

Cancel the common factor.

$3 e^{- (\frac{\ln (2)}{5 \cdot 1143} \cdot (5 \cdot 200))}$

Step 4.5

Rewrite the expression.

$3 e^{- (\frac{\ln (2)}{1143} \cdot 200)}$

Step 5

Combine $\frac{\ln (2)}{1143}$ and $200$ .

$3 e^{- \frac{\ln (2) \cdot 200}{1143}}$

Step 6

Move $200$ to the left of $\ln (2)$ .

$3 e^{- \frac{200 \ln (2)}{1143}}$