SOLUTION: Show that the sum of n terms of the progression log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.

Algebra.Com
Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Found 3 solutions by Edwin McCravy, ikleyn, mccravyedwin:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
I did not understand the problem, so I deleted what I thought it meant.
Ikleyn's solution is correct.  Notice that I changed the wording of the original
problem to her edited wording.  I think we tutors should change the wording of the
original problem whenever it is not easily understandable as written.

Edwin
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
Show that the sum of the end term of the progression Log x, Log x^2, Log x^3, log x^4 = n (n+1/2) Log x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        Wording and writing in the post are incorrect,  so I edited it to make sense from nonsense.

        My edited formulation is as follows:

                Show that the sum of n terms of the progression  log(x),  log(x^2),  log(x^3),  log(x^4) , . . ,  log(x^n)  is  (n*(n+1)/2)*log x.

        Below is my solution for this edited formulation. 


In this problem, x > 0.


Let a = log(x).


Then  = 2a,   = 3a, . . . and so on . . . till   = n*a.


Therefore, our progression takes the form

    a + 2a + 3a + . . . + n*a = (1 + 2 + 3 + . . . + n)*a.


The sum in parentheses in the right side is well known sum of the arithmetic progression,

and it is equal to  .


Thus   +  +  + . . . +  = .


It is the final answer, and the proof is complete.

Solved.



Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!
Ikleyn's solution is correct as she interpreted it.  Sometimes English is not
the first language of the student, and the way they translate things into English
is not always the same way we express things in the US.

Edwin
RELATED QUESTIONS

log... (answered by mukhopadhyay)
Given that {{{log(2,(x))}}} = m and {{{log(2,(y))}}} = n, express in terms of m and n: (answered by AnlytcPhil)
What is the value of the given expression: log sq.rt.(m^3/n) a. 1/2 log m - log n (answered by Jk22)
Given that {{{(log(m,((x^2)y)))=n}}} and {{{(log(m,((x)/(y^2))))=p}}}, express... (answered by Alan3354)
If log (subscript b)M=x and log (subscript b)N=y, express the following in terms of x and (answered by user_dude2008,stanbon)
Given that {{{log (x^2y) = n}}} and {{{log (x/y^2) = p}}}, express {{{log (x/y)}}} in... (answered by greenestamps)
if log x/log 4=n then what is... (answered by josmiceli)
For each of the following equations either prove that it is correct (by using the rules... (answered by venugopalramana)
Write as a single logarithm a) 2 log 5 log b b) 3 log x + 1/2 log y c) 2 log m + log n (answered by lwsshak3)