Solve 4^-2k=1/4

$$4 ^ { - 2 k } = \frac { 1 } { 4 }$$

Solve for k

$$k=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$4^{-2k}=\frac{1}{4}$$

Take the logarithm of both sides of the equation.

$$\log(4^{-2k})=\log(\frac{1}{4})$$

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

$$-2k\log(4)=\log(\frac{1}{4})$$

Divide both sides by \log(4).

$$-2k=\frac{\log(\frac{1}{4})}{\log(4)}$$

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

$$-2k=\log_{4}\left(\frac{1}{4}\right)$$

Divide both sides by -2.

$$k=-\frac{1}{-2}$$