Solve 3^3-2x=27

$$3 ^ { 3 - 2 x } = 27$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(3).

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

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

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

Subtract 3 from both sides of the equation.

$$-2x=3-3$$

Divide both sides by -2.

$$x=\frac{0}{-2}$$

Solve for x (complex solution)

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

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