Solve 2^x+2^x=2^18

$${ 2 }^{ x } + { 2 }^{ x } = { 2 }^{ 18 }$$

Solve for x

$$x=17$$

Steps Using Definition of Logarithm

Combine 2^{x} and 2^{x} to get 2\times 2^{x}.

$$2\times 2^{x}=2^{18}$$

Calculate 2 to the power of 18 and get 262144.

$$2\times 2^{x}=262144$$

Divide both sides by 2.

$$2^{x}=\frac{262144}{2}$$

Divide 262144 by 2 to get 131072.

$$2^{x}=131072$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(131072)$$

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

$$x\log(2)=\log(131072)$$

Divide both sides by \log(2).

$$x=\frac{\log(131072)}{\log(2)}$$

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

$$x=\log_{2}\left(131072\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+17$$

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