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Expert: Alon Mandes - 4/15/2009


Question
1. 2 ln x =1
2. ln(5-2x)=3
3. ln x +ln(x-1)=1
4. ln(ln x)=1


Answer
Ok, let's review some of the facts concering Ln function :
1. Ln(e)=1
2. Ln(ab)=Ln(a)+Ln(b)
3. Ln(e^x)=x
4. Ln(x²)=2Ln(x) & Ln(x³)=3Ln(x)
5. If Ln(x)=y then x=e^y
6. e^[Ln(x)]=1

Ok, lets start:
a) 2Ln(x)=1 -> Ln(x)=½ -> x=e^(½)=√e=1.648
  I used fact number 5
b) Ln(5-2x)=3 -> 52-x=e³ -> x=52-e³=52-20.08=29.91
  Again fact nber 5
c) Ln(x)+Ln(x-1)=1 -> Ln(x[x-1])=1 -> x[x-1]=e -> x²-x-e=0 ->
  x1=(½)[1+√(1+4e)]=2.22   &   x2=(½)[1-√(1+4e)]=-1.22
  I used fact number 2 , & fact number 5
d) Ln(Ln(x))=1 -> Ln(x)=e^1 -> x=e^e=15.15
  I used fact number 6 & fact number 5

Alon.  

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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