Solve 3^2x-4=1

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

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).

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

Add 4 to both sides of the equation.

$$2x=-\left(-4\right)$$

Divide both sides by 2.

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