Precalculus Examples

$7.5 = \frac{15}{1 + 2 e^{- 0.5 n}}$

Step 1

Simplify.

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Step 1.1

Multiply each term in $7.5 = \frac{15}{1 + 2 e^{- 0.5 n}}$ by $15$ .

$7.5 \cdot 15 = \frac{15}{1 + 2 e^{- 0.5 n}} \cdot 15$

Step 1.2

Multiply $7.5$ by $15$ .

$112.5$

Step 1.3

Reduce by cancelling the common factors.

$112.5 = e^{- 0.5 n}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(112.5)$ equals the exponent $(- 0.5 n)$ .

$\log_{e} (112.5) = - 0.5 n$