Solve 3^(12-3x)=729

$$3 ^ { ( 12 - 3 x ) } = 729$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$3^{-3x+12}=729$$

Take the logarithm of both sides of the equation.

$$\log(3^{-3x+12})=\log(729)$$

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

$$\left(-3x+12\right)\log(3)=\log(729)$$

Divide both sides by \log(3).

$$-3x+12=\frac{\log(729)}{\log(3)}$$

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

$$-3x+12=\log_{3}\left(729\right)$$

Subtract 12 from both sides of the equation.

$$-3x=6-12$$

Divide both sides by -3.

$$x=-\frac{6}{-3}$$

Solve for x (complex solution)

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

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