Solve 36^x=216

$${ 36 }^{ x } = 216$$

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.

$$36^{x}=216$$

Take the logarithm of both sides of the equation.

$$\log(36^{x})=\log(216)$$

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

$$x\log(36)=\log(216)$$

Divide both sides by \log(36).

$$x=\frac{\log(216)}{\log(36)}$$

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

$$x=\log_{36}\left(216\right)$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(6)}+\frac{3}{2}$$

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