Evaluate 5e^(2x+11)=30

$5 e^{2 x + 11} = 30$

Divide each term in $5 e^{2 x + 11} = 30$ by $5$ and simplify.

Divide each term in $5 e^{2 x + 11} = 30$ by $5$ .

$\frac{5 e^{2 x + 11}}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 e^{2 x + 11}}{5} = \frac{30}{5}$

Divide $e^{2 x + 11}$ by $1$ .

$e^{2 x + 11} = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$e^{2 x + 11} = 6$

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

$\ln (e^{2 x + 11}) = \ln (6)$

Expand the left side.

Expand $\ln (e^{2 x + 11})$ by moving $2 x + 11$ outside the logarithm.

$(2 x + 11) \ln (e) = \ln (6)$

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

$(2 x + 11) \cdot 1 = \ln (6)$

Multiply $2 x + 11$ by $1$ .

$2 x + 11 = \ln (6)$

Subtract $11$ from both sides of the equation.

$2 x = \ln (6) - 11$

Divide each term in $2 x = \ln (6) - 11$ by $2$ and simplify.

Divide each term in $2 x = \ln (6) - 11$ by $2$ .

$\frac{2 x}{2} = \frac{\ln (6)}{2} + \frac{- 11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\ln (6)}{2} + \frac{- 11}{2}$

Divide $x$ by $1$ .

$x = \frac{\ln (6)}{2} + \frac{- 11}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\ln (6)}{2} - \frac{11}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (6)}{2} - \frac{11}{2}$

Decimal Form:

$x = - 4.60412026 \dots$