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Math Help - Log Questions

  1. #1
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    Log Questions

    Hi,

    I'm needing help with solving two equations using logarithms:

    1) 15000=702.712(1.067)^x

    I know by "plugging and chugging" into x, the it's somewhere around 48. However, I'd like to know how to solve it the real way. Here's what I'm trying:

    Take the log of both sides log 15000 = log 702.712 (1.067) ^ x
    Drag the x out front 4.176 = (x) log 702.712 (1.067)

    But when I try to solve it any further, I get x equaling around 1 or 2... not right at all.

    Am I solving this equation wrong?




    Also, there is one more involving Pe^rt (continuous growth formula)

    2) 60000 = 10000e^.062t

    Because this equation involves e, I take the natural log of both sides:

    ln 60000 = ln 10000 e ^ .062 t

    I drag .062t out front:

    ln 60000 = (.062t) ln 10000

    I divide by ln 10000:

    1.1945 = .062 t

    Divide by .062,

    19.266 = t

    That's all good, I managed to solve the entire equation, except the teacher specifically told us our answer should come out between t= 25 and t=30. I think the answer should be around t=29


    So, I have two equations here. I know what the answer SHOULD be, but it really frustrates me that I can't solve them and come up with the answer myself. Can you guys point out where I might be going wrong?

    Thanks,
    Ethan
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by EthanDavis View Post
    Hi,

    I'm needing help with solving two equations using logarithms:

    1) 15000=702.712(1.067)^x

    I know by "plugging and chugging" into x, the it's somewhere around 48. However, I'd like to know how to solve it the real way. Here's what I'm trying:

    Take the log of both sides log 15000 = log 702.712 (1.067) ^ x
    Drag the x out front 4.176 = (x) log 702.712 (1.067)

    But when I try to solve it any further, I get x equaling around 1 or 2... not right at all.

    Am I solving this equation wrong?
    you can't drag the x out like that... first divide both sides by 702.712, then log both sides...

    so, 21.34587 = 1.067^x

    \Rightarrow \log 21.34587 = \log 1.067^x

    \Rightarrow \log 21.34587 = x \log 1.067

    now continue...
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by EthanDavis View Post
    Also, there is one more involving Pe^rt (continuous growth formula)

    2) 60000 = 10000e^.062t

    Because this equation involves e, I take the natural log of both sides:

    ln 60000 = ln 10000 e ^ .062 t

    I drag .062t out front:

    ln 60000 = (.062t) ln 10000

    I divide by ln 10000:

    1.1945 = .062 t

    Divide by .062,

    19.266 = t
    do the same thing i did in the first. as i said, you cannot drag out the power as you did. you have the log of a product, you'd have to separate them before bring down the power. it's much easier to just divide first, so on one side you have just a number to a power, no constant multiplier in front
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  4. #4
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    Jan 2008
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    Thank you,

    Those were both very silly mistakes. I will remember to divide before pulling the exponent out front.

    The answers came out right. Now I'm embarrassed!

    Thank you very much!
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