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  1. #1
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    [SOLVED] Showing?

    Given that 2^a = 3^b = 18^c, show that ab = c(b + 2a)
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by mark1950 View Post
    Given that 2^a = 3^b = 18^c, show that ab = c(b + 2a)
    2^a=3^b

    aln(2)=b ln(3)

    ln(3)=\frac{a ln(2)}{b} .....(1)


    3^b=18^c

    3^b=(2(3)^2)^c

    b ln(3) = c ln(2 (3^2))

    b ln(3) = c(ln(2) + 2ln(3) ) since ln(AB) = ln(A) + ln(B)

    sub the value of ln(3) from (1)

    b\left(\frac{a ln(2)}{b}\right) = c(ln(2) + 2\left(\frac{a ln(2)}{b}\right)

    b\left(a ln(2)\right) = cbln(2) + 2c\left(a ln(2)\right) by multiply with b


    b\left(a \right) = cb + 2c\left(a \right) division by ln(2)

    ba = c(b+2a)
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  3. #3
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    What does ln means? Can I use log instead of ln? Will it be the same?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mark1950 View Post
    What does ln means? Can I use log instead of ln? Will it be the same?
    \ln denotes the natural log, but for this any base of logarithm can be used. \log often denotes a logarithm to the base 10, but just as often denotes a natural logarithm or a logarithm to an unspecified base, so yes you can use \log.

    (any base will do for this problem)

    CB
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