Calculus/logs

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Expert: Alon Mandes - 12/12/2008


Question
Can you possibly help me? I've been asked to simplify 2logx - 4log3 + 5logy

Not only have I no idea what that means, I have no idea how to come to a solution. Any help would be greatly appreciated.


Many Thanks,
Ken

Answer
Let's refresh our memory with the facts regarding Log function :
1. Log(a*b)=Log(a)+Log(b)
2. Log(a/b)=Log(a)-Log(b)
3. Log(a^b)=a*Log(b)
Now,the form 2Log(x)-4Log(3)+5Log(y) will become
Log(x^2)-Log(3^4)+Log(y^5) according to rule (3).
Log(x^2)-Log(3^4) will become Log([(x^2)/81]) according to rule (2).
Log([(x^2)/81]+5Log(y) will become Log( [(x^2)/81]*(y^5) ) according
to rule (1).
So, our final answer will be : Log[(x^2)(y^5)/81].

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Alon Mandes

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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 .

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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".

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

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

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