Solve 4^3x=7

$$4 ^ { 3 x } = 7$$

Solve for x

$$x=\frac{\log_{2}\left(7\right)}{6}\approx 0.467892487$$

Steps Using Definition of Logarithm

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

$$4^{3x}=7$$

Take the logarithm of both sides of the equation.

$$\log(4^{3x})=\log(7)$$

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

$$3x\log(4)=\log(7)$$

Divide both sides by \log(4).

$$3x=\frac{\log(7)}{\log(4)}$$

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

$$3x=\log_{4}\left(7\right)$$

Divide both sides by 3.

$$x=\frac{\log_{2}\left(7\right)}{2\times 3}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(7\right)}{6}$$

$$n_{1}\in \mathrm{Z}$$