log-x-x-2-2-x-3-3-x-4-4-

Question Number 130553 by Study last updated on 26/Jan/21

l o g (x + \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots .) = ?

Answered by Dwaipayan Shikari last updated on 26/Jan/21

l o g (- l o g (1 - x)) = l o g (l o g (\frac{1}{1 - x}))

Commented by Study last updated on 26/Jan/21

l o g (\frac{1}{1 - x}) = ?

Commented by Study last updated on 26/Jan/21

w h y d i d y o u w r i t e - l o g (1 - x) d i r e c t l y ?

Commented by mr W last updated on 27/Jan/21

\ln (1 + x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + \dots

r e p l a c e x w i t h - x

\ln (1 - x) = - x - \frac{x^{2}}{2} - \frac{x^{3}}{3} - \frac{x^{4}}{4} - \dots

\Rightarrow - \ln (1 - x) = x + \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots

\Rightarrow \ln \frac{1}{1 - x} = x + \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots

Commented by Study last updated on 27/Jan/21

{l o g}_{x^{4} + x^{2} + x + 1} (x + \frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \dots .) = ?

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