Solve 3=(2)^frac{x{8}}

$$3 = ( 2 ) ^ { \frac { x } { 8 } }$$

Solve for x

$$x=8\log_{2}\left(3\right)\approx 12.679700006$$

Steps Using Definition of Logarithm

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

$$2^{\frac{x}{8}}=3$$

Use the rules of exponents and logarithms to solve the equation.

$$2^{\frac{1}{8}x}=3$$

Take the logarithm of both sides of the equation.

$$\log(2^{\frac{1}{8}x})=\log(3)$$

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

$$\frac{1}{8}x\log(2)=\log(3)$$

Divide both sides by \log(2).

$$\frac{1}{8}x=\frac{\log(3)}{\log(2)}$$

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

$$\frac{1}{8}x=\log_{2}\left(3\right)$$

Multiply both sides by 8.

$$x=\frac{\log_{2}\left(3\right)}{\frac{1}{8}}$$

Solve for x (complex solution)

$$x=\frac{16\pi n_{1}i}{\ln(2)}+8\log_{2}\left(3\right)$$

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