Solve for x 6*e^x=25

$6 \cdot e^{x} = 25$

Step 1

Divide each term in $(6 \cdot e^{x}) = 25$ by $6$ and simplify.

Divide each term in $(6 \cdot e^{x}) = 25$ by $6$ .

$\frac{(6 \cdot e^{x})}{6} = \frac{25}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 \cdot e^{x}}{6} = \frac{25}{6}$

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

$e^{x} = \frac{25}{6}$

Step 2

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

$\ln (e^{x}) = \ln (\frac{25}{6})$

Step 3

Expand the left side.

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

$x \ln (e) = \ln (\frac{25}{6})$

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

$x \cdot 1 = \ln (\frac{25}{6})$

Multiply $x$ by $1$ .

$x = \ln (\frac{25}{6})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (\frac{25}{6})$

Decimal Form:

$x = 1.42711635 \dots$