Solve 2^-x=4.9

$$2 ^ { - x } = 4.9$$

Solve for x

$$x=\log_{2}\left(\frac{10}{49}\right)\approx -2.292781749$$

Steps Using Definition of Logarithm

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

$$2^{-x}=4.9$$

Take the logarithm of both sides of the equation.

$$\log(2^{-x})=\log(4.9)$$

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

$$-x\log(2)=\log(4.9)$$

Divide both sides by \log(2).

$$-x=\frac{\log(4.9)}{\log(2)}$$

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

$$-x=\log_{2}\left(4.9\right)$$

Divide both sides by -1.

$$x=\frac{\ln(\frac{49}{10})}{-\ln(2)}$$