Solve 3(2^x)=2^x+16

$$3 ( 2 ^ { x } ) = 2 ^ { x } + 16$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

Subtract 2^{x} from both sides.

$$3\times 2^{x}-2^{x}=16$$

Combine 3\times 2^{x} and -2^{x} to get 2\times 2^{x}.

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

Divide both sides by 2.

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

Divide 16 by 2 to get 8.

$$2^{x}=8$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(8)$$

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

$$x\log(2)=\log(8)$$

Divide both sides by \log(2).

$$x=\frac{\log(8)}{\log(2)}$$

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

$$x=\log_{2}\left(8\right)$$

Solve for x (complex solution)

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

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