Solve 4*2^x=2^x+4

$$4 \times { 2 }^{ x } = { 2 }^{ x } +4$$

Solve for x

$$x=-\log_{2}\left(3\right)+2\approx 0.415037499$$

Steps Using Definition of Logarithm

Subtract 2^{x} from both sides.

$$4\times 2^{x}-2^{x}=4$$

Combine 4\times 2^{x} and -2^{x} to get 3\times 2^{x}.

$$3\times 2^{x}=4$$

Divide both sides by 3.

$$2^{x}=\frac{4}{3}$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(\frac{4}{3})$$

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

$$x\log(2)=\log(\frac{4}{3})$$

Divide both sides by \log(2).

$$x=\frac{\log(\frac{4}{3})}{\log(2)}$$

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

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

Solve for x (complex solution)

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

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