Solve 3^3x=27

$$3 ^ { 3 x } = 27$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$3^{3x}=27$$

Take the logarithm of both sides of the equation.

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

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

$$3x\log(3)=\log(27)$$

Divide both sides by \log(3).

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

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

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

Divide both sides by 3.

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

Solve for x (complex solution)

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

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