Solve for x 5*e^x=18

$5 \cdot e^{x} = 18$

Step 1

Divide each term in $(5 \cdot e^{x}) = 18$ by $5$ and simplify.

Divide each term in $(5 \cdot e^{x}) = 18$ by $5$ .

$\frac{(5 \cdot e^{x})}{5} = \frac{18}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \cdot e^{x}}{5} = \frac{18}{5}$

Divide $e^{x}$ by $1$ .

$e^{x} = \frac{18}{5}$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) = \ln (\frac{18}{5})$

Step 3

Expand the left side.

Expand $\ln (e^{x})$ by moving $x$ outside the logarithm.

$x \ln (e) = \ln (\frac{18}{5})$

The natural logarithm of $e$ is $1$ .

$x \cdot 1 = \ln (\frac{18}{5})$

Multiply $x$ by $1$ .

$x = \ln (\frac{18}{5})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (\frac{18}{5})$

Decimal Form:

$x = 1.28093384 \dots$