Question

I need help please. Find the exact solution to the equation54(1/3)^x = 2

Answer 1

x = 3

Explanations:

Given the indices expression

`54((1)/(3))^x=2`

Divide both sides of the equation by 54 to have:

`\begin{gathered} (54)/(54)((1)/(3))^x=\frac{\cancel{2}}{\cancel{54}} \\ ((1)/(3))^x=(1)/(27) \\ \end{gathered}`

Write in the inverse form to have:

`\begin{gathered} 3^(-x)=(1)/(3^3) \\ 3^(-x)=3^(-3) \end{gathered}`

Canceling the base

`\begin{gathered} \cancel{3}^(-x)=\cancel{3}^(-3) \\ -x=-3 \\ x=3 \end{gathered}`

Hence the value of x from the given equation is 3