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What is limit x tends to 0 log(1+x)/x to the base a?
Dear Aditya,
The value tends to 1.
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Aman Bansal
Askiitian Expert
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
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
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)
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.
the limit is 1( use L''Hospital''s rule to solve)
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