Solve (1/3)^-x=27

$$( \frac { 1 } { 3 } ) ^ { - x } = 27$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$\left(\frac{1}{3}\right)^{-x}=27$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{3}\right)^{-x})=\log(27)$$

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

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

Divide both sides by \log(\frac{1}{3}).

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

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

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

Divide both sides by -1.

$$x=-\frac{3}{-1}$$

Solve for x (complex solution)

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

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