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Math Help - Three logarithm, questions I would appreciate explained

  1. #1
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    Three logarithm, questions I would appreciate explained

    Hello I have three logarithm questions, I would very much appreciate it if someone could explain how to solve them, thank you.

    1. 2x+3=3x-4
    2. log7(x+1)3=2
    3. 3000=2000(1.01)​4t
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  2. #2
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    Re: Three logarithm, questions I would appreciate explained

    Hey AwkwardRaven.

    What log laws (and exponential laws) have you been taught?

    Also you should show us any partial attempts you have taken because it shows effort on your part and it makes our job which is to help you much easier.
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  3. #3
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    Re: Three logarithm, questions I would appreciate explained

    The properties of logarithms and the change of base rule.

    for #1 I tried: log2(x+3)=log2(x-4) but after that I'm kind of stuck. I'm not sure how to separate the x from the +3 and -4.
    Last edited by AwkwardRaven; December 6th 2012 at 08:00 PM.
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  4. #4
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    Re: Three logarithm, questions I would appreciate explained

    That is in-correct: you should use the fact that log_a(b) = log_x(b)/log_x(a) where x and a are bases.

    From this you get x+3 = (x-4)/log_2(3) and you can re-arrange to get x.
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  5. #5
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    Re: Three logarithm, questions I would appreciate explained

    ok so i need to make the 2 and 3 the same Utilizing the change of base rule?
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  6. #6
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    Re: Three logarithm, questions I would appreciate explained

    Yes, since you have two different bases.
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  7. #7
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    Re: Three logarithm, questions I would appreciate explained

    so i have log(x+3)/log2=log(x-4)/log3 ?
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  8. #8
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    Re: Three logarithm, questions I would appreciate explained

    No it's even simpler than that: recall that log_a(a^y) = y * log_a(a) = y.
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