Solve 4^3k=6

$$4 ^ { 3 k } = 6$$

Solve for k

$$k=\frac{\log_{2}\left(6\right)}{6}\approx 0.430827083$$

Steps Using Definition of Logarithm

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

$$4^{3k}=6$$

Take the logarithm of both sides of the equation.

$$\log(4^{3k})=\log(6)$$

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

$$3k\log(4)=\log(6)$$

Divide both sides by \log(4).

$$3k=\frac{\log(6)}{\log(4)}$$

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

$$3k=\log_{4}\left(6\right)$$

Divide both sides by 3.

$$k=\frac{\log_{2}\left(6\right)}{2\times 3}$$