Solve 2e^3x+4=90

$$2 e ^ { 3 x } + 4 = 90$$

Solve for x

$$x=\frac{\ln(43)}{3}\approx 1.253733372$$

Steps Using Definition of Logarithm

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

$$2e^{3x}+4=90$$

Subtract 4 from both sides of the equation.

$$2e^{3x}=86$$

Divide both sides by 2.

$$e^{3x}=43$$

Take the logarithm of both sides of the equation.

$$\log(e^{3x})=\log(43)$$

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

$$3x\log(e)=\log(43)$$

Divide both sides by \log(e).

$$3x=\frac{\log(43)}{\log(e)}$$

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

$$3x=\log_{e}\left(43\right)$$

Divide both sides by 3.

$$x=\frac{\ln(43)}{3}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3}+\frac{\ln(43)}{3}$$

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