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Thread: This is driving me crazy!!!! LOGS!!

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

    $\displaystyle 3^{4-3x}=4^{x+5}$

    $\displaystyle 4log3 - 3xlog3 = xlog4 + 5log4$

    $\displaystyle -3xlog3 - xlog4 = 5log4 - 4log3$

    $\displaystyle x(-3log3 - log4) = 5log4 - 4log3$

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

    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
    MHF Contributor 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!

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

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

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

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

    $\displaystyle x \;= \;\frac{5\log4 - 4\log3}{(-3\log3 - \log4)}$ . . . . 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: .$\displaystyle \log2 + 3$

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


    Press $\displaystyle \boxed{\text{log}}$ 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: .$\displaystyle \boxed{\text{log}}\;\;\boxed{2}\;\; \boxed{+}\;\;\boxed{3}\;\;\boxed{=}$
    . . the calculator reads it as: .log(2 + 3 =
    . . and returns: .log 5

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


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

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


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