Solve 144^x=12

$$144 ^ { x } = 12$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps Using Definition of Logarithm

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

$$144^{x}=12$$

Take the logarithm of both sides of the equation.

$$\log(144^{x})=\log(12)$$

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

$$x\log(144)=\log(12)$$

Divide both sides by \log(144).

$$x=\frac{\log(12)}{\log(144)}$$

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

$$x=\log_{144}\left(12\right)$$

Solve for x (complex solution)

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

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