Solve 3^3=3^4x+2

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

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps Using Definition of Logarithm

Calculate 3 to the power of 3 and get 27.

$$27=3^{4x+2}$$

Swap sides so that all variable terms are on the left hand side.

$$3^{4x+2}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{4x+2})=\log(27)$$

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

$$\left(4x+2\right)\log(3)=\log(27)$$

Divide both sides by \log(3).

$$4x+2=\frac{\log(27)}{\log(3)}$$

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

$$4x+2=\log_{3}\left(27\right)$$

Subtract 2 from both sides of the equation.

$$4x=3-2$$

Divide both sides by 4.

$$x=\frac{1}{4}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(3)}+\frac{1}{4}$$

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