Solve 5^2x+2=1/625

$$5 ^ { 2 x + 2 } = \frac { 1 } { 625 }$$

Solve for x

$$x=-3$$

Steps Using Definition of Logarithm

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

$$5^{2x+2}=\frac{1}{625}$$

Take the logarithm of both sides of the equation.

$$\log(5^{2x+2})=\log(\frac{1}{625})$$

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

$$\left(2x+2\right)\log(5)=\log(\frac{1}{625})$$

Divide both sides by \log(5).

$$2x+2=\frac{\log(\frac{1}{625})}{\log(5)}$$

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

$$2x+2=\log_{5}\left(\frac{1}{625}\right)$$

Subtract 2 from both sides of the equation.

$$2x=-4-2$$

Divide both sides by 2.

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