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Log Qn(Nottoo hard!)

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Answers:

confuzious

Sage

Karma Points: 4,039

Date Posted: 5/16/2008 10:41:34 AM Status: Live

Asker's Rating: Helpful

Response:

this is just a basic log rule:

ln(mⁿ) = n · ln(m)

in this case

ln(xⁿ) = n*ln(x)

Mr.Nash

Expert

Karma Points: 1,131

Date Posted: 5/16/2008 10:44:04 AM Status: Live

Asker's Rating: Helpful

Response:

we know, ln(A.B.C.....Z) = lnA+lnB+lnC+..........+lnZ

now,

ln(xⁿ) = ln[x.x.x..........x(n times)] = lnx+lnx+lnx+.........lnx(n times)

=n ln(x)

radne

Sage

Karma Points: 5,119

Date Posted: 5/16/2008 11:22:36 AM Status: Live

Asker's Rating: Lifesaver

Response:

Guessing they want you to prove this property?
[A] Uses induction, but also uses ln(ab)=ln(a)+ln(b), which may or may not be allowed
[B] Uses inverse properties of ln and e

[A] Proof By Induction
Assume that this is true

Show it that it's true for n=1

Show that it is true for n+1, that is we need to show that

Rewriting the exponent

Using ln(ab) = ln(a)+ln(b)

Using our assumption ln(xⁿ)=nln(x)

Factoring

Therefore, by induction

---------------------------------------------------------

[B] Proof by Inverse property of ln and e
We know that there exists some a such that

Rewritten another way, since e and ln are inverses

Raising both sides to n

Taking the ln of both sides

but a = ln(x), Therefore

matty888's Comment:

cheers san!!!!

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Log Qn(Nottoo hard!)

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