Solve 7+2^9-x=244

$$7 + 2 ^ { 9 - x } = 244$$

Solve for x

$$x=-\log_{2}\left(237\right)+9\approx 1.111256751$$

Steps Using Definition of Logarithm

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

$$2^{-x+9}+7=244$$

Subtract 7 from both sides of the equation.

$$2^{-x+9}=237$$

Take the logarithm of both sides of the equation.

$$\log(2^{-x+9})=\log(237)$$

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

$$\left(-x+9\right)\log(2)=\log(237)$$

Divide both sides by \log(2).

$$-x+9=\frac{\log(237)}{\log(2)}$$

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

$$-x+9=\log_{2}\left(237\right)$$

Subtract 9 from both sides of the equation.

$$-x=\log_{2}\left(237\right)-9$$

Divide both sides by -1.

$$x=\frac{\log_{2}\left(237\right)-9}{-1}$$

Solve for x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(2)}-\log_{2}\left(237\right)+9$$

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