Answer:
x = 3
Explanations:
Given the indices expression
[tex]54(\frac{1}{3})^x=2[/tex]
Divide both sides of the equation by 54 to have:
[tex]\begin{gathered} \frac{54}{54}(\frac{1}{3})^x=\frac{\cancel{2}}{\cancel{54}} \\ (\frac{1}{3})^x=\frac{1}{27} \\ \end{gathered}[/tex]
Write in the inverse form to have:
[tex]\begin{gathered} 3^{-x}=\frac{1}{3^3} \\ 3^{-x}=3^{-3} \end{gathered}[/tex]
Canceling the base
[tex]\begin{gathered} \cancel{3}^{-x}=\cancel{3}^{-3} \\ -x=-3 \\ x=3 \end{gathered}[/tex]
Hence the value of x from the given equation is 3
