Solve 5^a=1/25

$$5 ^ { a } = \frac { 1 } { 25 }$$

Solve for a

$$a=-2$$

Steps Using Definition of Logarithm

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

$$5^{a}=\frac{1}{25}$$

Take the logarithm of both sides of the equation.

$$\log(5^{a})=\log(\frac{1}{25})$$

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

$$a\log(5)=\log(\frac{1}{25})$$

Divide both sides by \log(5).

$$a=\frac{\log(\frac{1}{25})}{\log(5)}$$

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

$$a=\log_{5}\left(\frac{1}{25}\right)$$