Solve 2^1-x=6

$$2 ^ { 1 - x } = 6$$

Solve for x

$$x=-\log_{2}\left(3\right)\approx -1.584962501$$

Steps Using Definition of Logarithm

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

$$2^{-x+1}=6$$

Take the logarithm of both sides of the equation.

$$\log(2^{-x+1})=\log(6)$$

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

$$\left(-x+1\right)\log(2)=\log(6)$$

Divide both sides by \log(2).

$$-x+1=\frac{\log(6)}{\log(2)}$$

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

$$-x+1=\log_{2}\left(6\right)$$

Subtract 1 from both sides of the equation.

$$-x=\log_{2}\left(6\right)-1$$

Divide both sides by -1.

$$x=\frac{\log_{2}\left(6\right)-1}{-1}$$

Solve for x (complex solution)

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

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