Solve 16^x=64

$$16 ^ { x } = 64$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using Definition of Logarithm

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

$$16^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(16^{x})=\log(64)$$

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

$$x\log(16)=\log(64)$$

Divide both sides by \log(16).

$$x=\frac{\log(64)}{\log(16)}$$

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

$$x=\log_{16}\left(64\right)$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}+\frac{3}{2}$$

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