Solve 2^x=16384

$${ 2 }^{ x } =16384$$

Solve for x

$$x=14$$

Steps Using Definition of Logarithm

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

$$2^{x}=16384$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(16384)$$

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

$$x\log(2)=\log(16384)$$

Divide both sides by \log(2).

$$x=\frac{\log(16384)}{\log(2)}$$

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

$$x=\log_{2}\left(16384\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+14$$

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