Precalculus Examples

$5 e^{5 x} = 1685$

Step 1

Simplify.

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Step 1.1

Divide each term in $5 e^{5 x} = 1685$ by $5$ .

$\frac{5 e^{5 x}}{5} = \frac{1685}{5}$

Step 1.2

Divide $1685$ by $5$ .

$337$

Step 1.3

Reduce by cancelling the common factors.

$e^{5 x} = 337$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(337)$ equals the exponent $(5 x)$ .

$\log_{e} (337) = 5 x$