Solve 5^mdiv5^-3=5^3

$$5 ^ { m } \div 5 ^ { - 3 } = 5 ^ { 3 }$$

Solve for m

$$m=0$$

Steps Using Definition of Logarithm

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

$$125\times 5^{m}=125$$

Divide both sides by 125.

$$5^{m}=1$$

Take the logarithm of both sides of the equation.

$$\log(5^{m})=\log(1)$$

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

$$m\log(5)=\log(1)$$

Divide both sides by \log(5).

$$m=\frac{\log(1)}{\log(5)}$$

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

$$m=\log_{5}\left(1\right)$$