Solve 12^x*12^4=12^8

$$12 ^ { x } \times 12 ^ { 4 } = 12 ^ { 8 }$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

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

$$20736\times 12^{x}=429981696$$

Divide both sides by 20736.

$$12^{x}=20736$$

Take the logarithm of both sides of the equation.

$$\log(12^{x})=\log(20736)$$

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

$$x\log(12)=\log(20736)$$

Divide both sides by \log(12).

$$x=\frac{\log(20736)}{\log(12)}$$

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

$$x=\log_{12}\left(20736\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}+4$$

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