Precalculus Examples

$37.3 e^{0.017 x} = y$

Step 1

Simplify.

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Step 1.1

Divide each term in $37.3 e^{0.017 x} = y$ by $37.3$ .

$\frac{37.3 e^{0.017 x}}{37.3} = \frac{y}{37.3}$

Step 1.2

Multiply by $1$ .

$\frac{1 y}{37.3}$

Step 1.3

Factor $37.3$ out of $37.3$ .

$\frac{1 y}{37.3 (1)}$

Step 1.4

Separate fractions.

$\frac{1}{37.3} \cdot \frac{y}{1}$

Step 1.5

Divide $1$ by $37.3$ .

$0.02680965 \frac{y}{1}$

Step 1.6

Divide $y$ by $1$ .

$0.02680965 y$

Step 1.7

Reduce by cancelling the common factors.

$e^{0.017 x} = 0.02680965 y$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(0.02680965 y)$ equals the exponent $(0.017 x)$ .

$\log_{e} (0.02680965 y) = 0.017 x$