Solve 4(2^n)=2

$$4 ( 2 ^ { n } ) = 2$$

Solve for n

$$n=-1$$

Steps Using Definition of Logarithm

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

$$4\times 2^{n}=2$$

Divide both sides by 4.

$$2^{n}=\frac{1}{2}$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(2).

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

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

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