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

Aman Bansal
592 Points
11 years ago

The value tends to 1.

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Aman Bansal

29 Points
11 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

29 Points
11 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

Abhishekh kumar sharma
34 Points
11 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
11 years ago

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
11 years ago

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

shekhar
8 Points
10 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
3 years ago
Dear Student,