Solve for x -14+3e^x=11

$- 14 + 3 e^{x} = 11$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $14$ to both sides of the equation.

$3 e^{x} = 11 + 14$

Add $11$ and $14$ .

$3 e^{x} = 25$

Step 2

Divide each term in $3 e^{x} = 25$ by $3$ and simplify.

Divide each term in $3 e^{x} = 25$ by $3$ .

$\frac{3 e^{x}}{3} = \frac{25}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 e^{x}}{3} = \frac{25}{3}$

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

$e^{x} = \frac{25}{3}$

Step 3

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

$\ln (e^{x}) = \ln (\frac{25}{3})$

Step 4

Expand the left side.

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

$x \ln (e) = \ln (\frac{25}{3})$

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

$x \cdot 1 = \ln (\frac{25}{3})$

Multiply $x$ by $1$ .

$x = \ln (\frac{25}{3})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \ln (\frac{25}{3})$

Decimal Form:

$x = 2.12026353 \dots$