Solve 16^4k=66

$$16 ^ { 4 k } = 66$$

Solve for k

$$k=\frac{\log_{2}\left(66\right)}{16}\approx 0.377774632$$

Steps Using Definition of Logarithm

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

$$16^{4k}=66$$

Take the logarithm of both sides of the equation.

$$\log(16^{4k})=\log(66)$$

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

$$4k\log(16)=\log(66)$$

Divide both sides by \log(16).

$$4k=\frac{\log(66)}{\log(16)}$$

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

$$4k=\log_{16}\left(66\right)$$

Divide both sides by 4.

$$k=\frac{\log_{2}\left(66\right)}{4\times 4}$$