#### Answer

$x=243$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_{1/3} x=-5
,$ change the expression to exponential form. Then use the laws of exponents.
$\bf{\text{Solution Details:}}$
Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
\left(\dfrac{1}{3}\right)^{-5}=x
.\end{array}
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1^{-5}}{3^{-5}}=x
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3^{5}}{1^{5}}=x
\\\\
\dfrac{243}{1}=x
\\\\
x=243
.\end{array}