What is the solution to the equation (lny)^2 - 2ln(y^5) = 11, and how do you get the derivative of the equation with respect to y?

Question

anonymous · Answer

wait, why are you trying to do a derivative of the equation? this is a simple quadratic equation.

anonymous · Answer

Like as in -b(+-) sqrt b^2-4ac over 2a?

anonymous · Answer

what is 
$$\ln a ^{b}$$
?

anonymous · Answer

Oh, so I can just plug all of that into the quadratic equation to get my solution and then take the derivative?

anonymous · Answer

No, you dont need to take any derivatives at all.

anonymous · Answer

I'm so confused.

anonymous · Answer

just answer my question. what is 
$$\ln a ^{b}$$

anonymous · Answer

a^b?

anonymous · Answer

okay do you know about logarithms?

anonymous · Answer

A little. I had calculus last semester...and I'm having to refresh everything...lol. If I took the derivative of the equation you just gave me, then I would get a^b right?

anonymous · Answer

I didn't ask for the derivative of log a^b. I just asked what log a^b was.

anonymous · Answer

okay log a^b = b log a

anonymous · Answer

Oh! Yes.

anonymous · Answer

http://en.wikipedia.org/wiki/Logarithmic_identities#Algebraic_identities_or_laws

anonymous · Answer

do you know what logarithm means though?

anonymous · Answer

don't worry, thats a side question.

anonymous · Answer

Holy crap! So, really the problem should look like...$$((lny)^2)/(2lny^5)$$

anonymous · Answer

NO! how did you get THAT?

anonymous · Answer

(lny)^2 - 2lny^5 = 11
or (lny)^2 - 10 lny -11 = 0
say ln y = x
x^2-10x-11 =0
solve for x, substitute in ln y

anonymous · Answer

got it?

anonymous · Answer

need feedback to know you got it.

anonymous · Answer

Ohhh OKay I got it, I'm sorry for the delay. I was making dinner. That makes sense. See, I started dividing because I figured if you have ln (2-3) then it's ln 2/ln 3. Idk. I don't know why I thought that.