Solve 9^2x+2=27

$$9 ^ { 2 x + 2 } = 27$$

Solve for x

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

Steps Using Definition of Logarithm

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

$$9^{2x+2}=27$$

Take the logarithm of both sides of the equation.

$$\log(9^{2x+2})=\log(27)$$

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

$$\left(2x+2\right)\log(9)=\log(27)$$

Divide both sides by \log(9).

$$2x+2=\frac{\log(27)}{\log(9)}$$

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

$$2x+2=\log_{9}\left(27\right)$$

Subtract 2 from both sides of the equation.

$$2x=\frac{3}{2}-2$$

Divide both sides by 2.

$$x=-\frac{\frac{1}{2}}{2}$$

Solve for x (complex solution)

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

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