Precalculus Examples

$200 (x) = \frac{300}{1 + e^{- 3 x}}$

Step 1

Simplify.

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Step 1.1

Multiply $200$ by $x$ .

$200 x = \frac{300}{1 + e^{- 3 x}}$

Step 1.2

Multiply each term in $200 x = \frac{300}{1 + e^{- 3 x}}$ by $300$ .

$200 x \cdot 300 = \frac{300}{1 + e^{- 3 x}} \cdot 300$

Step 1.3

Multiply $300$ by $200$ .

$60000 x$

Step 1.4

Reduce by cancelling the common factors.

$60000 x = e^{- 3 x}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(60000 x)$ equals the exponent $(- 3 x)$ .

$\log_{e} (60000 x) = - 3 x$