Solve 11*3^2x+1=297

$$11 \times 3 ^ { 2 x + 1 } = 297$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$11\times 3^{2x+1}=297$$

Divide both sides by 11.

$$3^{2x+1}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x+1})=\log(27)$$

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

$$\left(2x+1\right)\log(3)=\log(27)$$

Divide both sides by \log(3).

$$2x+1=\frac{\log(27)}{\log(3)}$$

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

$$2x+1=\log_{3}\left(27\right)$$

Subtract 1 from both sides of the equation.

$$2x=3-1$$

Divide both sides by 2.

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

Solve for x (complex solution)

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

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