Solve 128*(1/2)^n=1/2

$$128 \times ( \frac { 1 } { 2 } ) ^ { n } = \frac { 1 } { 2 }$$

Solve for n

$$n=8$$

Steps Using Definition of Logarithm

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

$$128\times \left(\frac{1}{2}\right)^{n}=\frac{1}{2}$$

Divide both sides by 128.

$$\left(\frac{1}{2}\right)^{n}=\frac{1}{256}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{2}\right)^{n})=\log(\frac{1}{256})$$

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

$$n\log(\frac{1}{2})=\log(\frac{1}{256})$$

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

$$n=\frac{\log(\frac{1}{256})}{\log(\frac{1}{2})}$$

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

$$n=\log_{\frac{1}{2}}\left(\frac{1}{256}\right)$$