Solve 3^a=1/27

$$3 ^ { a } = \frac { 1 } { 27 }$$

Solve for a

$$a=-3$$

Steps Using Definition of Logarithm

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

$$3^{a}=\frac{1}{27}$$

Take the logarithm of both sides of the equation.

$$\log(3^{a})=\log(\frac{1}{27})$$

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

$$a\log(3)=\log(\frac{1}{27})$$

Divide both sides by \log(3).

$$a=\frac{\log(\frac{1}{27})}{\log(3)}$$

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

$$a=\log_{3}\left(\frac{1}{27}\right)$$