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anonymous
 one year ago
The variables x and y satisfy the equation (x)^ny=C, where n and C are constants. When x=1.10, y=5.20, and when x=3.20, y=1.05. (i) Find the values of n and C.
anonymous
 one year ago
The variables x and y satisfy the equation (x)^ny=C, where n and C are constants. When x=1.10, y=5.20, and when x=3.20, y=1.05. (i) Find the values of n and C.

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if we substitute your data, we get two different conditions, namely: \[\Large \begin{gathered} {\left( {1.1} \right)^n} \cdot 5.2 = C \hfill \\ \hfill \\ {\left( {3.2} \right)^n} \cdot 1.05 = C \hfill \\ \end{gathered} \] those equation are an algebraic system, which can be solved for n and C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not being able to solve _

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if I use the elimination method, I can write this: \[\Large {\left( {1.1} \right)^n} \cdot 5.2 = {\left( {3.2} \right)^n} \cdot 1.05\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, I divide both sides of that equation by (1.1)^n, so I get: \[\Large 5.2 = {\left( {\frac{{3.2}}{{1.1}}} \right)^n} \cdot 1.05\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then I divide both sides again by 1.05, so I can write this: \[\Large \frac{{5.2}}{{1.05}} = {\left( {\frac{{3.2}}{{1.1}}} \right)^n}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we got an exponential equation, which can be solved using logarithms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not getting the right answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know.. can you continue further ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if we take the logarithm in base 10, of both sides, we get: \[\Large \begin{gathered} n \cdot {\log _{10}}\left( {\frac{{3.2}}{{1.1}}} \right) = {\log _{10}}\left( {\frac{{5.2}}{{1.05}}} \right) \hfill \\ \hfill \\ n = \frac{{{{\log }_{10}}\left( {\frac{{5.2}}{{1.05}}} \right)}}{{{{\log }_{10}}\left( {\frac{{3.2}}{{1.1}}} \right)}} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0finally got the answer.. thank you very much
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