Solve 3^-q*1/27=81

$$3 ^ { - q } \times \frac { 1 } { 27 } = 81$$

Solve for q

$$q=-7$$

Steps Using Definition of Logarithm

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

$$\frac{1}{27}\times 3^{-q}=81$$

Multiply both sides by 27.

$$3^{-q}=2187$$

Take the logarithm of both sides of the equation.

$$\log(3^{-q})=\log(2187)$$

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

$$-q\log(3)=\log(2187)$$

Divide both sides by \log(3).

$$-q=\frac{\log(2187)}{\log(3)}$$

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

$$-q=\log_{3}\left(2187\right)$$

Divide both sides by -1.

$$q=\frac{7}{-1}$$