Solve (4^2)^2=4*4^x

$$( 4 ^ { 2 } ) ^ { 2 } = 4 \cdot 4 ^ { x }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4^{4}=4\times 4^{x}$$

Calculate 4 to the power of 4 and get 256.

$$256=4\times 4^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$4\times 4^{x}=256$$

Divide both sides by 4.

$$4^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(64)$$

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

$$x\log(4)=\log(64)$$

Divide both sides by \log(4).

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+3$$

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