Solve 2^4-2x=64

$$2 ^ { 4 - 2 x } = 64$$

Solve for x

$$x=-1$$

Steps Using Definition of Logarithm

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

$$2^{-2x+4}=64$$

Take the logarithm of both sides of the equation.

$$\log(2^{-2x+4})=\log(64)$$

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

$$\left(-2x+4\right)\log(2)=\log(64)$$

Divide both sides by \log(2).

$$-2x+4=\frac{\log(64)}{\log(2)}$$

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

$$-2x+4=\log_{2}\left(64\right)$$

Subtract 4 from both sides of the equation.

$$-2x=6-4$$

Divide both sides by -2.

$$x=\frac{2}{-2}$$