Solve 5^n-1=625

$$5 ^ { n - 1 } = 625$$

Solve for n

$$n=5$$

Steps Using Definition of Logarithm

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

$$5^{n-1}=625$$

Take the logarithm of both sides of the equation.

$$\log(5^{n-1})=\log(625)$$

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

$$\left(n-1\right)\log(5)=\log(625)$$

Divide both sides by \log(5).

$$n-1=\frac{\log(625)}{\log(5)}$$

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

$$n-1=\log_{5}\left(625\right)$$

Add 1 to both sides of the equation.

$$n=4-\left(-1\right)$$