Solve for x e^(4x)=5

$e^{4 x} = 5$

Step 1

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

$\ln (e^{4 x}) = \ln (5)$

Step 2

Expand the left side.

Expand $\ln (e^{4 x})$ by moving $4 x$ outside the logarithm.

$4 x \ln (e) = \ln (5)$

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

$4 x \cdot 1 = \ln (5)$

Multiply $4$ by $1$ .

$4 x = \ln (5)$

Step 3

Divide each term in $4 x = \ln (5)$ by $4$ and simplify.

Divide each term in $4 x = \ln (5)$ by $4$ .

$\frac{4 x}{4} = \frac{\ln (5)}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{\ln (5)}{4}$

Divide $x$ by $1$ .

$x = \frac{\ln (5)}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (5)}{4}$

Decimal Form:

$x = 0.40235947 \dots$