# 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
2 years, 3 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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

- 2 years, 3 months ago