Solve 5^n-3=1/25

$$5 ^ { n - 3 } = \frac { 1 } { 25 }$$

Solve for n

$$n=1$$

Steps Using Definition of Logarithm

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

$$5^{n-3}=\frac{1}{25}$$

Take the logarithm of both sides of the equation.

$$\log(5^{n-3})=\log(\frac{1}{25})$$

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

$$\left(n-3\right)\log(5)=\log(\frac{1}{25})$$

Divide both sides by \log(5).

$$n-3=\frac{\log(\frac{1}{25})}{\log(5)}$$

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

$$n-3=\log_{5}\left(\frac{1}{25}\right)$$

Add 3 to both sides of the equation.

$$n=-2-\left(-3\right)$$