MHB Natural Log Inequality: True or Misunderstanding?

tmt1
Messages
230
Reaction score
0
I was talking to my professor and she said that $(ln n)^a < n$ for all values of $a$. Is this true or was I misunderstanding?
 
Mathematics news on Phys.org
It's false. Consider $\ln^3\left(e^2\right)$ and note that $e^2\approx7.4$.
 
greg1313 said:
It's false. Consider $\ln^3\left(e^2\right)$ and note that $e^2\approx7.4$.

I forgot an important detail. This is in context of $n$ approaching infinity.
 
You 'forgot' that? You completely denied it when you said "for all n"!
 
This is essentially a question of limits - moved to Pre-Calculus.

tmt, do you think it's true? False? Explain your reasoning.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

B Can a log have multiple bases?
Replies
44
Views
4K
Relation between log function and its characteristic g
Replies
4
Views
1K
B Log(x), an easy and useful way to calculate it
Replies
10
Views
2K
B I do not understand Log tables
Replies
15
Views
3K
I Calculation of x from log equation
Replies
3
Views
1K
I What is the inequality for prime numbers in the Prime Number Theorem proof?
Replies
9
Views
2K
MHB Inequation with just 3 solutions
Replies
4
Views
2K
MHB Natural logs solve ln⁡((x-1)/(x-3))=2
Replies
3
Views
2K
MHB Finding the Domain of a Logarithmic Function f(x) = log_5(8 - 2x)
Replies
7
Views
2K
B How to express ##3^{\sqrt(2)}## in terms of natural logarithms
Replies
10
Views
1K

Hot Threads

Recent Insights

Back
Top