Solve 4^n=1024

$${ 4 }^{ n } =1024$$

Solve for n

$$n=5$$

Steps Using Definition of Logarithm

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

$$4^{n}=1024$$

Take the logarithm of both sides of the equation.

$$\log(4^{n})=\log(1024)$$

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

$$n\log(4)=\log(1024)$$

Divide both sides by \log(4).

$$n=\frac{\log(1024)}{\log(4)}$$

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

$$n=\log_{4}\left(1024\right)$$

Solve for n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(2)}+5$$

$$n_{1}\in \mathrm{Z}$$