Precalculus Examples

$f (- 2) = 5 e^{- 2}$

Step 1

Simplify.

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Step 1.1

Divide each term in $f (- 2) = 5 e^{- 2}$ by $5$ .

$\frac{f (- 2)}{5} = \frac{5 e^{- 2}}{5}$

Step 1.2

Move $- 2$ to the left of $f$ .

$\frac{- 2 f}{5}$

Step 1.3

Move the negative in front of the fraction.

$- \frac{2 f}{5}$

Step 1.4

Reduce by cancelling the common factors.

$- \frac{2 f}{5} = e^{- 2}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(- \frac{2 f}{5})$ equals the exponent $(- 2)$ .

$\log_{e} (- \frac{2 f}{5}) = - 2$