Waste less time on Facebook — follow Brilliant.

Logg'e' function to the base \(x\)

If \[y= \log_{x}e^{\log_{x}e^{.... \text{50 times}}}\]

Then find \(\dfrac{dy}{dx}\) at \(x=2\)

Note by Chinmay Sangawadekar
1 year, 5 months ago

No vote yet
1 vote


Sort by:

Top Newest

\[y= \log_{x}e^{\log_{x}e^{.... \text{50 times}}}=\log^{50}_{x}e=\frac{1}{\ln^{50}x} \\ \frac{dy}{dx}=-\frac{50\ln^{49}x\cdot \frac{1}{x} }{\ln ^{100}x}=-\frac{50}{x\ln^{51}x} \\ \frac{dy}{dx}|_{x=2}=-\frac{25}{\ln^{51}2}\]

Akshat Sharda - 1 year, 5 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...