Solve 4^4x+4=7

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

Solve for x

$$x=\frac{\log_{2}\left(3\right)}{8}\approx 0.198120313$$

Steps Using Definition of Logarithm

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

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

Subtract 4 from both sides of the equation.

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(4).

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

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

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

Divide both sides by 4.

$$x=\frac{\log_{2}\left(3\right)}{2\times 4}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(3\right)}{8}$$

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