Solve 125^2v=5^2

$$125 ^ { 2 v } = 5 ^ { 2 }$$

Solve for v

$$v=\frac{1}{3}\approx 0.333333333$$

Steps Using Definition of Logarithm

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

$$125^{2v}=25$$

Take the logarithm of both sides of the equation.

$$\log(125^{2v})=\log(25)$$

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

$$2v\log(125)=\log(25)$$

Divide both sides by \log(125).

$$2v=\frac{\log(25)}{\log(125)}$$

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

$$2v=\log_{125}\left(25\right)$$

Divide both sides by 2.

$$v=\frac{\frac{2}{3}}{2}$$