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Math Help - logs!!

  1. #1
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    logs!!

    4 times 2^x = 8 times 5^x solve for x
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  2. #2
    Junior Member
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    Quote Originally Posted by lbj2322 View Post
    4 times 2^x = 8 times 5^x solve for x
     4(2^x) = 8(5^x)

    Since both sides are equal, if we take the log of both sides, they remain equal. Assume the common (base 10) log

     log (4(2^x)) = log (8(5^x))

    Hopefully you know the properties of logs, and know how to re-write a log of a product:

      log 4 + log 2^x = log 8 + log 5^x

    Another property of logs lets you move the exponent

      log 4 + x log 2 = log 8 + x log 5

    We've now cleared the exponents. You should be able to move all the x's to the same side, and the other terms to the other side, and use basic algebra to get x by itself. Then use your calculator to compute the  log_{10} values.

    Note also, you can simplify the original equation by first dividing both sides by 4.
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