Solve 5^(2x-6)=1

$${ 5 }^{ (2x-6) } =1$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$5^{2x-6}=1$$

Take the logarithm of both sides of the equation.

$$\log(5^{2x-6})=\log(1)$$

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

$$\left(2x-6\right)\log(5)=\log(1)$$

Divide both sides by \log(5).

$$2x-6=\frac{\log(1)}{\log(5)}$$

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

$$2x-6=\log_{5}\left(1\right)$$

Add 6 to both sides of the equation.

$$2x=-\left(-6\right)$$

Divide both sides by 2.

$$x=\frac{6}{2}$$