Solve 512=2*2^x

$$512 = 2 \times { 2 }^{ x }$$

Solve for x

$$x=8$$

Steps Using Definition of Logarithm

Divide both sides by 2.

$$\frac{512}{2}=2^{x}$$

Divide 512 by 2 to get 256.

$$256=2^{x}$$

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

$$2^{x}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(256)$$

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

$$x\log(2)=\log(256)$$

Divide both sides by \log(2).

$$x=\frac{\log(256)}{\log(2)}$$

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

$$x=\log_{2}\left(256\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+8$$

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