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

$$log(x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+....)=?$$

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

$$log(-log(1-x))=log\left(log\left(\frac{1}{1-x}\right)\right)$$

Commented by Study last updated on 26/Jan/21

$$log\left(\frac{1}{1-x}\right)=?$$

Commented by Study last updated on 26/Jan/21

$$whydidyouwrite-log(1-x)directly?$$

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

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

Commented by Study last updated on 27/Jan/21

$${log}_{x^4+x^2+x+1}(x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+....)=?$$

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