The discussion revolves around simplifying an equation involving logarithmic expressions, specifically focusing on the equation y - 1 / 3 = 1 / 3 (x - ln(1/3)). Participants are examining the equivalence of this equation to the form x - 3y + (1 + ln3) = 0 as stated in a textbook.
Some participants have provided insights regarding the logarithmic identities used in the simplification process. There appears to be a recognition that the original poster's result and the textbook's answer are equivalent, although the original poster expresses confusion about the correctness of their solution.
There is an indication that the textbook's answer is considered correct, which raises questions about the assumptions made in the original poster's calculations. The discussion reflects a need for clarity on logarithmic properties and their application in the context of the problem.
Your result and the book answer are equivalent.nesan said:Homework Statement
y - 1 / 3 = 1 / 3 (x - ln(1/3))
The Attempt at a Solution
y - 1 / 3 = 1 / 3 (x - ln(1/3))
0 = 1 /3 x - 1/3 ln(1 / 3) + 1 / 3 - y
0 = x - ln(1 / 3) + 1 - 3y
I don't see any problem with it.
Text book says it's wrong. >_<
The answer is = x - 3y + (1 + ln3) = 0
Steely Dan said:You have pretty much the same thing, except that they have used
[tex]\text{ln}( 1/x ) = \text{ln}( x^{-1} ) = -\text{ln}(x)[/tex]
to convert [itex]\text{ln}(1/3)[/itex] to [itex]-\text{ln}(3)[/itex].
Thank you very much. :]SammyS said:Your result and the book answer are equivalent.
ln(1/3) = ln(3-1) = (-1) ln(3)