Solve 12^x=100

$$12 ^ { x } = 100$$

Solve for x

$$x=2\log_{12}\left(10\right)\approx 1.853256816$$

Steps Using Definition of Logarithm

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

$$12^{x}=100$$

Take the logarithm of both sides of the equation.

$$\log(12^{x})=\log(100)$$

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

$$x\log(12)=\log(100)$$

Divide both sides by \log(12).

$$x=\frac{\log(100)}{\log(12)}$$

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

$$x=\log_{12}\left(100\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}+2\log_{12}\left(10\right)$$

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