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Math Help - Help! Equations with exponets :(

  1. #1
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    Unhappy Help! Equations with exponets :(

    I would greatly appreciate if someone could help me on this one, thank you so much:

    Solve for x to eight decimal places if

    2^(2x – 1) = 3^(x-2)

    Substitute your x value answer
    back into original and show that it
    will make each side equal.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Alesa'7 View Post
    I would greatly appreciate if someone could help me on this one, thank you so much:

    Solve for x to eight decimal places if

    2^(2x 1) = 3^(x-2)

    Substitute your x value answer
    back into original and show that it
    will make each side equal.
    Hello!

    Note that 2^{2x-1}=3^{x-1}\implies 4^x 2^{-1}=3^x 3^{-1}\implies\left(\tfrac{4}{3}\right)^x=\tfrac{2}{3}  \implies x=\frac{\ln\left(\tfrac{2}{3}\right)}{\ln\left(\tf  rac{4}{3}\right)}

    Now you can plug this into your calculator and get an approximation to 8 decimal places.

    --Chris
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  3. #3
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    is it -1.40942084 ?
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  4. #4
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    lol sry for being nosy.. juss looking around at the different post,while I wait till someone helps with mine... This place is so cool
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