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Math Help - Logarithm equations

  1. #1
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    Smile Logarithm equations

    I have encountered an equation for logarithms and the guide in the book didn't make sense to me.
    Here's the equation: 3^(x+2)=4^(x-1)

    And here's how the book explained it:
    1) Take log of each side: log3^(x+2)=log4^(x-1)
    2)Take exponents to the front: x+2log3=x-1log4
    and here's where it starts not making sense to me,
    3)divide each side by 2log3: 2x=(-1log4)/(2log3)

    How did the equation suddenly become 2x and why wouldn't it become (x+2)log3=(x-1)log4?
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  2. #2
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    Quote Originally Posted by windia View Post
    I have encountered an equation for logarithms and the guide in the book didn't make sense to me.
    Here's the equation: 3^(x+2)=4^(x-1)
    How did the equation suddenly become 2x and why wouldn't it become (x+2)log3=(x-1)log4?
    The part in blue is correct.
    So use it to finish.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    3^(x+2)=4^(x-1)

    we take log from both sides:

    log3^(x+2)=log4^(x-1)

    (x+2)log3=(x-1)log4

    xlog3+2log3=xlog4-log4

    x(log3-log4)=-log4-2log3

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    .
    .
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  4. #4
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    Wow good thing I trusted my instincts. I'm through with this book haha. Thanks you guys
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