Precalculus Examples

$65 (1 + 271 e^{- 0.122}) = 90$

Step 1

Simplify.

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Step 1.1

Divide each term in $65 (1 + 271 e^{- 0.122}) = 90$ by $65$ .

$\frac{65 (1 + 271 e^{- 0.122})}{65} = \frac{90}{65}$

Step 1.2

Cancel the common factor of $90$ and $65$ .

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Step 1.2.1

Factor $5$ out of $90$ .

$\frac{5 (18)}{65}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $5$ out of $65$ .

$\frac{5 \cdot 18}{5 \cdot 13}$

Step 1.2.2.2

Cancel the common factor.

$\frac{5 \cdot 18}{5 \cdot 13}$

Step 1.2.2.3

Rewrite the expression.

$\frac{18}{13}$

Step 1.3

Reduce by cancelling the common factors.

$e^{- 0.122} = \frac{18}{13}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(\frac{18}{13})$ equals the exponent $(- 0.122)$ .

$\log_{e} (\frac{18}{13}) = - 0.122$