Solve 3^7-x=3

$$3 ^ { 7 - x } = 3$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

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

$$3^{-x+7}=3$$

Take the logarithm of both sides of the equation.

$$\log(3^{-x+7})=\log(3)$$

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

$$\left(-x+7\right)\log(3)=\log(3)$$

Divide both sides by \log(3).

$$-x+7=\frac{\log(3)}{\log(3)}$$

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

$$-x+7=\log_{3}\left(3\right)$$

Subtract 7 from both sides of the equation.

$$-x=1-7$$

Divide both sides by -1.

$$x=-\frac{6}{-1}$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(3)}+6$$

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