Solve 4^v-3=1/4

$$4 ^ { v - 3 } = \frac { 1 } { 4 }$$

Solve for v

$$v=2$$

Steps Using Definition of Logarithm

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

$$4^{v-3}=\frac{1}{4}$$

Take the logarithm of both sides of the equation.

$$\log(4^{v-3})=\log(\frac{1}{4})$$

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

$$\left(v-3\right)\log(4)=\log(\frac{1}{4})$$

Divide both sides by \log(4).

$$v-3=\frac{\log(\frac{1}{4})}{\log(4)}$$

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

$$v-3=\log_{4}\left(\frac{1}{4}\right)$$

Add 3 to both sides of the equation.

$$v=-1-\left(-3\right)$$