Solve 3^4-x=2

$$3 ^ { 4 - x } = 2$$

Solve for x

$$x=-\log_{3}\left(2\right)+4\approx 3.369070246$$

Steps Using Definition of Logarithm

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

$$3^{-x+4}=2$$

Take the logarithm of both sides of the equation.

$$\log(3^{-x+4})=\log(2)$$

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

$$\left(-x+4\right)\log(3)=\log(2)$$

Divide both sides by \log(3).

$$-x+4=\frac{\log(2)}{\log(3)}$$

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

$$-x+4=\log_{3}\left(2\right)$$

Subtract 4 from both sides of the equation.

$$-x=\log_{3}\left(2\right)-4$$

Divide both sides by -1.

$$x=\frac{\log_{3}\left(2\right)-4}{-1}$$

Solve for x (complex solution)

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

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