Precalculus Examples

$10 = \frac{12.57}{1 + 4.11 e^{- 0.026 x}}$

Step 1

Simplify.

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Step 1.1

Multiply each term in $10 = \frac{12.57}{1 + 4.11 e^{- 0.026 x}}$ by $12.57$ .

$10 \cdot 12.57 = \frac{12.57}{1 + 4.11 e^{- 0.026 x}} \cdot 12.57$

Step 1.2

Multiply $10$ by $12.57$ .

$125.7$

Step 1.3

Reduce by cancelling the common factors.

$125.7 = e^{- 0.026 x}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(125.7)$ equals the exponent $(- 0.026 x)$ .

$\log_{e} (125.7) = - 0.026 x$