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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.

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  1. anonymous
    • one year ago
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    \[x ^{n}y=C\]

  2. anonymous
    • one year ago
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    @Michele_Laino

  3. Michele_Laino
    • one year ago
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    if 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

  4. Michele_Laino
    • one year ago
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    equations*

  5. anonymous
    • one year ago
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    not being able to solve -_-

  6. Michele_Laino
    • one year ago
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    if I use the elimination method, I can write this: \[\Large {\left( {1.1} \right)^n} \cdot 5.2 = {\left( {3.2} \right)^n} \cdot 1.05\]

  7. anonymous
    • one year ago
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    yesss

  8. Michele_Laino
    • one year ago
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    now, I divide both sides of that equation by (1.1)^n, so I get: \[\Large 5.2 = {\left( {\frac{{3.2}}{{1.1}}} \right)^n} \cdot 1.05\]

  9. Michele_Laino
    • one year ago
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    then I divide both sides again by 1.05, so I can write this: \[\Large \frac{{5.2}}{{1.05}} = {\left( {\frac{{3.2}}{{1.1}}} \right)^n}\]

  10. anonymous
    • one year ago
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    okay

  11. Michele_Laino
    • one year ago
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    we got an exponential equation, which can be solved using logarithms

  12. anonymous
    • one year ago
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    not getting the right answer

  13. Michele_Laino
    • one year ago
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    why?

  14. anonymous
    • one year ago
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    i dont know.. can you continue further ?

  15. Michele_Laino
    • one year ago
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    ok!

  16. Michele_Laino
    • one year ago
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    if we take the logarithm in base 10, of both sides, we get: \[\Large \begin{gathered} n \cdot {\log _{10}}\left( {\frac{{3.2}}{{1.1}}} \right) = {\log _{10}}\left( {\frac{{5.2}}{{1.05}}} \right) \hfill \\ \hfill \\ n = \frac{{{{\log }_{10}}\left( {\frac{{5.2}}{{1.05}}} \right)}}{{{{\log }_{10}}\left( {\frac{{3.2}}{{1.1}}} \right)}} \hfill \\ \end{gathered} \]

  17. Michele_Laino
    • one year ago
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    what do you get?

  18. anonymous
    • one year ago
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    finally got the answer.. thank you very much

  19. Michele_Laino
    • one year ago
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    thanks! :)

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