Solve 27^x=3^12

$$27 ^ { x } = 3 ^ { 12 }$$

Solve for x

$$x=4$$

Steps Using Definition of Logarithm

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

$$27^{x}=531441$$

Take the logarithm of both sides of the equation.

$$\log(27^{x})=\log(531441)$$

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

$$x\log(27)=\log(531441)$$

Divide both sides by \log(27).

$$x=\frac{\log(531441)}{\log(27)}$$

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

$$x=\log_{27}\left(531441\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(3)}+4$$

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