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    It's part (iv) of the question that I'm having problems with. The function f is defined by:

    \mathrm{f(x) =} \frac{1}{3} \ln (\frac{x - a}{2})

    (iv) Given that \mathrm{f(a^3) - f(a^2)} = \ln \frac{5}{3}, find the exact value of a.

    So this is what I did:
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    So my answer was a = 125/27. But the answer in the back is a = 98/27. I have no idea how I would get that? I've noticed the book has a few errors, so is this just an error or am I going wrong somewhere?

    Thanks very much!
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     a^3 - a is NOT  a^2 (they are not 'like' terms)

    Would the log rule  log(a) - log(b) = log(a/b) help you?
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    (Original post by InadequateJusticex)
     a^3 - a is NOT  a^2 (they are not 'like' terms)

    Would the log rule  log(a) - log(b) = log(a/b) help you?
    Thank you - I realise that I just wasn't thinking properly!

    I'll have another go.
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    (Original post by AlesanaWill)
    It's part (iv) of the question that I'm having problems with. The function f is defined by:

    \mathrm{f(x) =} \frac{1}{3} \ln (\frac{x - a}{2})

    (iv) Given that \mathrm{f(a^3) - f(a^2)} = \ln \frac{5}{3}, find the exact value of a.

    So this is what I did:
    Name:  Untitled.jpg
Views: 93
Size:  365.8 KB

    So my answer was a = 125/27. But the answer in the back is a = 98/27. I have no idea how I would get that? I've noticed the book has a few errors, so is this just an error or am I going wrong somewhere?

    Thanks very much!

    a^3 - a does not equal a^2
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    (Original post by steve2005)
    a^3 - a does not equal a^2
    Yes I realised that mistake. But now I've got:

    1/3ln (a^3- a / a^2 - a) = ln 5/3

    which becomes:

    (a^3 -a / a^2 - a) = 125/27

    and I'm not getting anywhere. I divided the top and bottom of the fraction by a and then put it into a quadratic equation but that's not helping either. Help?
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    (Original post by AlesanaWill)
    Yes I realised that mistake. But now I've got:

    1/3ln (a^3- a / a^2 - a) = ln 5/3

    which becomes:

    (a^3 -a / a^2 - a) = 125/27

    and I'm not getting anywhere. I divided the top and bottom of the fraction by a and then put it into a quadratic equation but that's not helping either. Help?
    Difference of two squares
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    Thanks very much all. Sorted now.
 
 
 
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