Solve for x e^(3x)+5=6

$e^{3 x} + 5 = 6$

Step 1

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

Subtract $5$ from both sides of the equation.

$e^{3 x} = 6 - 5$

Subtract $5$ from $6$ .

$e^{3 x} = 1$

Step 2

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

$\ln (e^{3 x}) = \ln (1)$

Step 3

Expand the left side.

Expand $\ln (e^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (e) = \ln (1)$

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

$3 x \cdot 1 = \ln (1)$

Multiply $3$ by $1$ .

$3 x = \ln (1)$

Step 4

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$3 x = 0$

Step 5

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$