Solve 2^4^2=2^x

$$2 ^ { 4 ^ { 2 } } = 2 ^ { x }$$

Solve for x

$$x=16$$

Steps Using Definition of Logarithm

Calculate 4 to the power of 2 and get 16.

$$2^{16}=2^{x}$$

Calculate 2 to the power of 16 and get 65536.

$$65536=2^{x}$$

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

$$2^{x}=65536$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(65536)$$

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

$$x\log(2)=\log(65536)$$

Divide both sides by \log(2).

$$x=\frac{\log(65536)}{\log(2)}$$

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

$$x=\log_{2}\left(65536\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+16$$

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