Solve for n 4e^(2n-5)+3=11

$4 e^{2 n - 5} + 3 = 11$

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

Subtract $3$ from both sides of the equation.

$4 e^{2 n - 5} = 11 - 3$

Subtract $3$ from $11$ .

$4 e^{2 n - 5} = 8$

Divide each term in $4 e^{2 n - 5} = 8$ by $4$ and simplify.

Divide each term in $4 e^{2 n - 5} = 8$ by $4$ .

$\frac{4 e^{2 n - 5}}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 e^{2 n - 5}}{4} = \frac{8}{4}$

Divide $e^{2 n - 5}$ by $1$ .

$e^{2 n - 5} = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$e^{2 n - 5} = 2$

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

$\ln (e^{2 n - 5}) = \ln (2)$

Expand the left side.

Expand $\ln (e^{2 n - 5})$ by moving $2 n - 5$ outside the logarithm.

$(2 n - 5) \ln (e) = \ln (2)$

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

$(2 n - 5) \cdot 1 = \ln (2)$

Multiply $2 n - 5$ by $1$ .

$2 n - 5 = \ln (2)$

Add $5$ to both sides of the equation.

$2 n = \ln (2) + 5$

Divide each term in $2 n = \ln (2) + 5$ by $2$ and simplify.

Divide each term in $2 n = \ln (2) + 5$ by $2$ .

$\frac{2 n}{2} = \frac{\ln (2)}{2} + \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{\ln (2)}{2} + \frac{5}{2}$

Divide $n$ by $1$ .

$n = \frac{\ln (2)}{2} + \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$n = \frac{\ln (2)}{2} + \frac{5}{2}$

Decimal Form:

$n = 2.84657359 \dots$