SOLUTION: Suppose that x=ln(A) and y=ln(B). Write the following formula in terms of x and y ln(A-B)=? Hi everyone, I have been struggling with trying to figure out how to solve this

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Question 1203539: Suppose that x=ln(A) and y=ln(B). Write the following formula in terms of x and y
ln(A-B)=?

Hi everyone, I have been struggling with trying to figure out how to solve this. Any help and explaining how you solved it would be helpful :)
Found 3 solutions by math_tutor2020, ikleyn, MathLover1:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

One log rule is ln(A)-ln(B) = ln(A/B)

But there isn't a log rule for ln(A-B)

I think there might be a typo in your textbook.

I suppose this could be one pathway to take, but it's a bit convoluted and messy.
x = ln(A)
y = ln(B)
A = e^x
B = e^y
A-B = e^x - e^y
A-B = e^x(1 - e^(y-x))
Ln[A-B] = Ln[ e^x(1 - e^(y-x)) ]
Ln[A-B] = Ln[e^x] + Ln[1 - e^(y-x) ]
Ln[A-B] = 1 + Ln[1 - e^(y-x)]
But we run into the same problem of having a log of the form Ln(something - somethingElse)

Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website!
.

There is NO general formula for ln(A-B) in terms of x= ln(A) and y= ln(B).

Such general formula DOES NOT EXIST, so leave your hopes to get such a formula.

Who is your teacher/professor, who assigned it to you ?

Did you invent this assignment on your own for yourselves?

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

=>
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=> this is only what you can do to express the formula in terms of and