Ln (a+b) + ln (a-b) - 2 ln c?

The questions wants you to express the quanity as a single logarithm. I got stuck towards the end.





ln (a+b) + ln (a-b) - 2 ln c


ln a + ln b + lna -lnb - 2lnc


2 ln a - 2 lnc





I am stuck here. Any help is appreciated.

Ln (a+b) + ln (a-b) - 2 ln c?
ln (a+b)(a-b)/c^2





Rules of logarithm that I used





ln x + ln y = ln xy


ln x - ln y = ln x/y


n ln x = ln x^n





What you did wrong was separate the (a+b) and the (a-b). These values are expressed as a single quantity. Therefore you are not allowed to separate this values - they don't follow the rules of logarithm.
Reply:First thing you have to be careful of when doing these questions is that ln (a+b) IS NOT ln a + ln b





Try it with a calculator ln(1+1)=ln(2) will not be equal ln(1)+ln(1)





here is a few nice tips for you


ln(4)+ln(5)=ln(4 X 5)


ln(4)-ln(5)=ln(4/5)


5ln(6)=ln(6)^5





try solving it now








If all else fails the answer is ln[(a+b)X(a-b)/(c^2)]

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