Solve (1/2)^2x+4=1/64

$$( \frac { 1 } { 2 } ) ^ { 2 x + 4 } = \frac { 1 } { 64 }$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$\left(\frac{1}{2}\right)^{2x+4}=\frac{1}{64}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{2}\right)^{2x+4})=\log(\frac{1}{64})$$

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

$$\left(2x+4\right)\log(\frac{1}{2})=\log(\frac{1}{64})$$

Divide both sides by \log(\frac{1}{2}).

$$2x+4=\frac{\log(\frac{1}{64})}{\log(\frac{1}{2})}$$

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

$$2x+4=\log_{\frac{1}{2}}\left(\frac{1}{64}\right)$$

Subtract 4 from both sides of the equation.

$$2x=6-4$$

Divide both sides by 2.

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