Express y as Function of x?

Express y as a function of x. The constant C is a positive number.





(1) In y = In(x + C)





(2) In y = 2In x - In(x + 1) + InC

Express y as Function of x?
1. since you have ln on both sides, you can "remove it".





ln a = ln b, then a = b





therefore





y = x + C





2. you have to simplify the RHS using the properties of logarithms.





it gives you:





ln (x^2) - ln (x + 1) + ln C = ln (x^2)/(x+1) + ln C =


ln (Cx^2) / (x + 1)





so you have:





ln y = ln (Cx^2) / (x + 1), and just like in 1. you can remove ln:





y = (C*x^2) / (x + 1)





check properties of logarithms here:


http://www.google.com/search?q=propertie...





Cheers,





Kempos
Reply:(1) =%26gt; e^(ln y) = e^ (ln(x + C))


=%26gt; y = x + C





(2) =%26gt; ln y = ln(x^2) - ln(x + 1) + ln C


=%26gt; ln y = ln([(x^2)*C]/[x + 1])


=%26gt; y = C(x^2)/(x+1)





Not sure how clear this is... will be much clearer on paper, but hope this helps...

statice