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I am trying to show that the following relation holds:

\begin{equation} \log(1+ax) = log(x) + o(log(x)) \end{equation} as $x\rightarrow \infty$, where $a$ a positive number. I tried using Taylor expansion but I could not come to the results. Any hints would be really helpful! Thanks!

SpawnKilleR
  • 641

1 Answers1

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$$\log(1 + ax) = \log\left(x\left(\frac 1x + a\right)\right) = \log x + \log\left(\frac 1x + a\right)$$

Tunococ
  • 10,303