Precalculus Examples

$\frac{1}{2} = 150000 e^{- 0.142 \cdot 12}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Multiply $- 0.142$ by $12$ .

$\frac{1}{2} = 150000 e^{- 1.704}$

Step 1.2

Divide each term in $\frac{1}{2} = 150000 e^{- 1.704}$ by $150000$ .

$\frac{\frac{1}{2}}{150000} = \frac{150000 e^{- 1.704}}{150000}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{150000}$

Step 1.4

Multiply $\frac{1}{2} \cdot \frac{1}{150000}$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{1}{2}$ by $\frac{1}{150000}$ .

$\frac{1}{2 \cdot 150000}$

Step 1.4.2

Multiply $2$ by $150000$ .

$\frac{1}{300000}$

Step 1.5

Reduce by cancelling the common factors.

$\frac{1}{300000} = e^{- 1.704}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(\frac{1}{300000})$ equals the exponent $(- 1.704)$ .

$\log_{e} (\frac{1}{300000}) = - 1.704$