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  1. #1

    Another Log Problem: logY^3 = logx(x+4)^2

    Hello all

    I have another log problem which I was hoping someone could help me with.

    I have the following:-

    logY^3 = logx(x+4)^2

    I have been told that the above statement is the same as:-

    Y^3 = x(x+4)

    The bit I don't understand is where does the log go?
    What law allows the log to be removed from both sides?

    Can anyone help?

    Thank you.

    (assume base 10 log)

  2. #2
    Quote Originally Posted by Ted_Grendy View Post
    Hello all

    I have another log problem which I was hoping someone could help me with.

    I have the following:-

    logY^3 = logx(x+4)^2

    I have been told that the above statement is the same as:-

    Y^3 = x(x+4)^2

    The bit I don't understand is where does the log go?
    What law allows the log to be removed from both sides?

    Can anyone help?

    Thank you.

    (assume base 10 log)
    If log A = log B then A = B.
    Heavens to Murgatroyd!!

  3. #3
    Senior Member
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    Quote Originally Posted by Ted_Grendy View Post
    Hello all

    I have another log problem which I was hoping someone could help me with.

    I have the following:-

    logY^3 = logx(x+4)^2

    I have been told that the above statement is the same as:-

    Y^3 = x(x+4)

    The bit I don't understand is where does the log go?
    What law allows the log to be removed from both sides?

    Can anyone help?

    Thank you.

    (assume base 10 log)
    It sounds so good, I'll repeat it again: If log A = log B, then A = B
    Last edited by Jomo; 12-05-2018 at 10:43 PM.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  4. #4
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    If log(u) = log(v) then u = v
    I'm a man of few words...but I use 'em often!!

  5. #5
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    Quote Originally Posted by Denis View Post
    If log(u) = log(v) then u = v
    You have start off slow with some students and use A's and B's before U's and V's. Didn't they teach you nuttin in business school
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  6. #6
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    Quote Originally Posted by Jomo View Post
    Didn't they teach you nuttin in business school
    You forgot to end your sentence with a "?"
    Didn't they teach you nuttin in grammar school
    I'm a man of few words...but I use 'em often!!

  7. #7
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    Quote Originally Posted by Denis View Post
    You forgot to end your sentence with a "?"
    Didn't they teach you nuttin in grammar school
    I'm an American. So no, they did not teach me anything in grammar school.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  8. #8
    Quote Originally Posted by Jomo View Post
    It sounds so good, I'll repeat it again: If log A = log B, then A = B
    Jomo, If you "repeat it again" doesn't that mean that you are saying it for the nth time where n>=3 ?
    Heavens to Murgatroyd!!

  9. #9
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    Quote Originally Posted by Ted_Grendy View Post
    Hello all

    I have another log problem which I was hoping someone could help me with.

    I have the following:-

    logY^3 = logx(x+4)^2

    I have been told that the above statement is the same as:-

    Y^3 = x(x+4)

    The bit I don't understand is where does the log go?
    What law allows the log to be removed from both sides?

    Can anyone help?

    Thank you.

    (assume base 10 log)
    Log (for any base) is an increasing function which means that if A < B, then it must be that Log(A) < Log(B). So if A and B are different values it can't be that Log(A) = Log(B). But if Log(A) = Log(B), then yes A = B. In fact if A=B and they are both positive, then Log(A) = Log(B)

    Note: If you have something like Log(-2) = Log (x) we can NOT conclude that x=-2 because Log(-2) makes no sense (you can't take the log of 0 or a negative number).
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  10. #10
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    Quote Originally Posted by Ted_Grendy View Post
    Hello all

    I have another log problem which I was hoping someone could help me with.

    I have the following:-

    logY^3 = logx(x+4)^2

    I have been told that the above statement is the same as:-

    Y^3 = x(x+4)

    The bit I don't understand is where does the log go?
    What law allows the log to be removed from both sides?

    Can anyone help?

    Thank you.

    (assume base 10 log)
    This question belongs in intermediate algebra or perhaps even pre-calculus, but it is an excellent question.

    Logarithm functions, regardless of base, are members of a class of functions known as invertible. There is a theorem that proves

    [tex]\text {If } f(x) \text { is invertible, then } f(x) = f(y) \implies x = y.[/tex]

    It can be shown that logs are invertible (in my youth, when logs were actually used for computations, we had to work with the inverse called an antilog).

    But if you do not want to work through the proof that logs are invertible, a proof that is very advanced, you can just say that one of the laws of logarithms is

    [tex]log_a(x) = log_a(y) \implies x = y.[/tex]
    Last edited by JeffM; 12-06-2018 at 09:28 AM.

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