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Math Help - Exponents (x and 2x)??

  1. #1
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    Exponents (x and 2x)??

    I can't solve this for the life of me; help ?

    2.71 = (1.0915)^(-x) + 3(1.0915)^(-2x)
    How do we solve such equations? I can't factor because I'm left with an x in my exponent ... I'm stumped.
    Is there even a solution?
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  2. #2
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    Did you try?

     2.71 = 1.0915^{-x} + 3(1.0915)^{-2x}

     2.71 = 1.0915^{-x} + 3((1.0915)^{-x}\times (1.0915)^{2})

    Oops, sorry that ain't right!
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  3. #3
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    I honestly did and I can't figure out any way to isolate x. Am I missing something plainly obvious here??
    I tried to factor out (1.0915)^x, but that didn't solve the problem at all.

    Isn't that equal to (1.0915)^(2-x) however? Exponents add??
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  4. #4
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    Yep that was a boo boo on my behalf.

    Might have to solve this one numerically. I'll have a think about it.
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  5. #5
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    Thank you very much!
    (What does numerically mean??)
    I'm in my first university year just to let you know - it's possible that I perhaps got the equation wrong from the problem too. So don't go to too much trouble, just wondered if I was missing something obvious!
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  6. #6
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    I have found a solution numerically \approx 2.575
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  7. #7
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    Quote Originally Posted by Volcanicrain View Post
    Thank you very much!
    (What does numerically mean??)
    I just put the equation in an excel sheet and tried a list of different numbers.
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  8. #8
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    Thank, that does work.
    Now I'll figure out how to prove it. Thanks =)
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  9. #9
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    Quote Originally Posted by Volcanicrain View Post
    2.71 = (1.0915)^(-x) + 3(1.0915)^(-2x)
    Make your life easier: let k = 1.0915; then you have:
    k^(-x) + 3k^(-2x) = 2.71
    Get rid of minuses:
    1/k^x + 3/k^(2x) = 2.71
    Multiply by k^(2x):
    k^x + 3 = 2.71k^(2x)
    Rearrange;
    2.71(k^x)^2 - k^x - 3 = 0

    You now have a quadratic...can you finish it?

    You may find it easier to let a = k^x; then:
    2.71a^2 - a - 3 = 0 : get my drift?
    Solve for a; then 1.0915^x = a ; x = log(a) / log(1.0915)
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  10. #10
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    Quote Originally Posted by Wilmer View Post
    Make your life easier: let k = 1.0915; then you have:
    k^(-x) + 3k^(-2x) = 2.71

    You now have a quadratic...can you finish it?
    *kicks myself*
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  11. #11
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    Wow thank you Wilmer!
    I was playing around with the idea of a quadratic... I was trying to complete a square or something but had not thought of that.
    It makes perfect sense to remove the negative exponents by multiplying by k^2x all across.
    I am really grateful for your answer!! Thank you so much!
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  12. #12
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    Quote Originally Posted by pickslides View Post
    *kicks myself*
    Ah gee Picks, I've done that so often I decided
    to buy felt shoes...hurts less
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