Solve 3^2x+4=1

$${ 3 }^{ 2x+4 } =1$$

Solve for x

$$x=-2$$

Steps Using Definition of Logarithm

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

$$3^{2x+4}=1$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x+4})=\log(1)$$

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

$$\left(2x+4\right)\log(3)=\log(1)$$

Divide both sides by \log(3).

$$2x+4=\frac{\log(1)}{\log(3)}$$

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

$$2x+4=\log_{3}\left(1\right)$$

Subtract 4 from both sides of the equation.

$$2x=-4$$

Divide both sides by 2.

$$x=-\frac{4}{2}$$