Solve 3^-x2=7

$${ 3 }^{ -x2 } =7$$

Solve for x_2

$$x_{2}=-\log_{3}\left(7\right)\approx -1.771243749$$

Steps Using Definition of Logarithm

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

$$3^{-x_{2}}=7$$

Take the logarithm of both sides of the equation.

$$\log(3^{-x_{2}})=\log(7)$$

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

$$-x_{2}\log(3)=\log(7)$$

Divide both sides by \log(3).

$$-x_{2}=\frac{\log(7)}{\log(3)}$$

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

$$-x_{2}=\log_{3}\left(7\right)$$

Divide both sides by -1.

$$x_{2}=\frac{\log_{3}\left(7\right)}{-1}$$