Solve 2^n=10^6

$$2 ^ { n } = 10 ^ { 6 }$$

Solve for n

$$n=6\log_{2}\left(10\right)\approx 19.931568569$$

Steps Using Definition of Logarithm

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

$$2^{n}=1000000$$

Take the logarithm of both sides of the equation.

$$\log(2^{n})=\log(1000000)$$

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

$$n\log(2)=\log(1000000)$$

Divide both sides by \log(2).

$$n=\frac{\log(1000000)}{\log(2)}$$

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

$$n=\log_{2}\left(1000000\right)$$