Solve 3^x3=27^-1

$${ 3 }^{ x3 } = { 27 }^{ -1 }$$

Solve for x_3

$$x_{3}=-3$$

Steps Using Definition of Logarithm

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

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(3).

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

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

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