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Math Help - Log Equations help please!

  1. #1
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    Log Equations help please!

    1. A mammal's resting metabloic rate (R), in kilocalories per day, is related to its mass, m, in kilograms, by the equation
    logR=log73.3 +0.75 log m. Predict the mass of a wolf with a resting metabloic rate of 1050 Kcal/day

    2. Mahal invests $500 in an account with an annual percentage rate of 5% compounded quartely. How long will it take for Mahal's single investment to double in value?
    b) Mahal invests $500 at the end of every 3 months in an accountant with an annual percentage rate of 4.8% compounded quarterly. How long will it take for Mahal's investment to be worth 100,000? Use FV= R[(1+i)^n-1] / i
    where FV= future value, n is the number of equal periodic payments of R dollars, and i is the interest rate per compounding period expressed as a decimal

    Please any help
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Log Equations help please!

    1.) You want to solve the equation:

    \log(R)=\log(73.3)+0.75\log(m)

    for m.

    Have you any thoughts on what steps you should take to do this?
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  3. #3
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    Re: Log Equations help please!

    i tried subtracting log(73.3) then divide by .75 didnt, then second log didnt work or maybe i made a calculator error if that is correct
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Log Equations help please!

    Yes, those are good first steps which gives you:

    \log(m)=\frac{4}{3}\left(\log(R)-\log(73.3) \right)

    Now, is there a property of logs that will allow us to combine the two log terms on the right?
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  5. #5
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    Re: Log Equations help please!

    (4/3) (logR / log(73.3)) = log m ?
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  6. #6
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    Re: Log Equations help please!

    oh i got it, i cant seem to get the interest ones though
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Log Equations help please!

    You are not properly using the logarithmic property you want, the property you want to use is:

    \log_a(b)-\log_a(c)=\log_a\left(\frac{b}{c} \right)

    Can you use this to rewrite the equation?
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  8. #8
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    Re: Log Equations help please!

    Not quite, but you are close. You should end up with a single log term on each side.
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