Solve 5e^3x=15

$$5 e ^ { 3 x } = 15$$

Solve for x

$$x=\frac{\ln(3)}{3}\approx 0.366204096$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$5e^{3x}=15$$

Divide both sides by 5.

$$e^{3x}=3$$

Take the logarithm of both sides of the equation.

$$\log(e^{3x})=\log(3)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$3x\log(e)=\log(3)$$

Divide both sides by \log(e).

$$3x=\frac{\log(3)}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$3x=\log_{e}\left(3\right)$$

Divide both sides by 3.

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

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3}+\frac{\ln(3)}{3}$$

$$n_{1}\in \mathrm{Z}$$