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What is limit x tends to 0 log(1+x)/x to the base a?

What is limit x tends to 0  log(1+x)/x to the base a?


 

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8 Answers

Aman Bansal
592 Points
8 years ago

Dear Aditya,

The value tends to 1.

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Aman Bansal

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chandradeep pokhariya
29 Points
8 years ago

Just we have to expand the f(x) i.e. we can write it ltx~> 0 log a (1+x)- lt x~>o log a x

                                             So by using the expansion of log(1+x) and value of log a (0) i.e. 1 we get answer -1

chandradeep pokhariya
29 Points
8 years ago

Here we will use the expansion method 

Firstly limx-0 loga(1+x)/x

firstly using log property we get:

limx-0loga(1+x)-logx

then we change the base of log i.e limx-0 {loge(1+x)/logea}-logax

then adter using expansion of loge(1+x) we get answer " 1/logea

Abhishekh kumar sharma
34 Points
8 years ago

we know x→0 log(1+x)/x=1 but when the base is (e) here base is (a) so

after changing base to (e) we get the

answer   1/log a     to the base (e)

Akash Kumar Dutta
98 Points
8 years ago

Dear Aditya,

its a very simple question.
apply the expansion of log.( log 1+x = x - x^2/2 +x^3/3 .......to infinity)
and we get ans as 1/log a to the base e.

Regards.

Gautham Pai M K
35 Points
8 years ago

the limit is 1( use L''Hospital''s rule to solve)

shekhar
8 Points
7 years ago
ques :- if x tends to infinity what is d value of logx/x ?? plz solve dis step by step and also write the values if applied
Rishi Sharma
askIITians Faculty 646 Points
11 months ago
Dear Student,
Please find below the solution to your problem.

apply the expansion of log.( log 1+x = x - x^2/2 +x^3/3 .......to infinity)
and we get ans as 1/log a to the base e.

Thanks and Regards

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