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Math Help - This is driving me crazy!!!! LOGS!!

  1. #1
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    This is driving me crazy!!!! LOGS!!

    3^{4-3x}=4^{x+5}

    4log3 - 3xlog3 = xlog4 + 5log4

    -3xlog3 - xlog4 = 5log4 - 4log3

    x(-3log3 - log4) = 5log4 - 4log3

    x = \frac{5log4 - 4log3}{(-3log3 - log4)}

    My answer is completely wrong, apparently it's -0.542 so i guess theres something up with my factorising?
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  2. #2
    Super Member ebaines's Avatar
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    You have it right

    Your answer is indeed -0.542. Why do you think you have it wrong?
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  3. #3
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    I was putting it into the calculator incorrectly.. oops!
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  4. #4
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    Hello, Flexible!

    3^{4-3x}\;=\;4^{x+5}

    4\log3 - 3x\log3 \;=\; x\log4 + 5\log4

    -3x\log3 - x\log4 \;=\; 5\log4 - 4\log3

    x(-3\log3 - \log4) \;=\; 5\log4 - 4\log3

    x \;= \;\frac{5\log4 - 4\log3}{(-3\log3 - \log4)} . . . . All of this is correct!

    My answer is completely wrong.
    Apparently it's -0.542

    I bet you're entering it incorrectly into your calculator.


    Suppose we want: . \log2 + 3

    If we enter: . \boxed{\text{log}}\;\;\boxed{2}\;\;\boxed{+}\;\;\b  oxed{3}\;\;\boxed{=} ... we will get the wrong answer.


    Press \boxed{\text{log}} on your calculator.
    . . On the display you will see: .log(
    It automatically provides a left parenthesis in ancitipation of a longer quantity.
    . . We are expected to provide the right parenthesis.

    If we don't ... and we press: . \boxed{\text{log}}\;\;\boxed{2}\;\;   \boxed{+}\;\;\boxed{3}\;\;\boxed{=}
    . . the calculator reads it as: .log(2 + 3 =
    . . and returns: .log 5

    We must enter: . \boxed{\text{log}}\;\;\boxed{2}\;\;{\color{blue}\b  oxed{)}}\;\;\boxed{+}\;\;\boxed{3}\;\;\boxed{=}


    So an expression like: . 5\log4 - 4\log3 should be treated like this:

    . . \boxed{5}\;\;\boxed{\times}\;\;\boxed{\text{log}} \;\;\boxed{4} \;\;{\color{red}\boxed{)}}\;\;\boxed{-}\;\;\boxed{4}\;\;\boxed{\times}\;\;\boxed{\text{l  og}}\;\;\boxed{3}\;\;{\color{red}\boxed{)}}


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