To solve an odd problem using tetration

  • Context: Undergrad 
  • Thread starter Thread starter Frogeyedpeas
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the expression e^{\sqrt[3]{y}} and the application of tetration to eliminate radicals. Users explore whether applying tetration of order 3 can transform the expression into a non-radical form. It is concluded that simple tetration does not yield a non-radical expression, as evidenced by attempts to compute ln(x)^3. The consensus is that further exploration is needed to find a suitable transformation.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with tetration and its mathematical implications
  • Knowledge of logarithmic functions, specifically natural logarithms
  • Basic concepts of radical expressions and their simplifications
NEXT STEPS
  • Research the properties and applications of tetration in advanced mathematics
  • Explore alternative methods for simplifying radical expressions
  • Study the relationship between logarithmic and exponential functions
  • Investigate numerical methods for evaluating complex expressions
USEFUL FOR

Mathematicians, students studying advanced calculus, and anyone interested in exploring the complexities of exponential and radical expressions.

Frogeyedpeas
Messages
80
Reaction score
0
Given the expression:

[itex]e^{\sqrt[3]{y}}[/itex]

What numerical operator must this expression undergo to make it so that there are no radicals in the expression.

Would a simple tetration to the order 3 finish the job? Whenever I try to tetrate the number It doesn't come out to a non-radical expression. Thanks guys
 
Last edited by a moderator:
Mathematics news on Phys.org
ln(x)^3
 

Similar threads

Undergrad Expressing any given point on plane with one unique number
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Five points in space with rational distances that are not co-linear
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Can this particular method solve these quadratic equations?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Find an explicit formula for this n-sum problem
  • · Replies 7 ·
Replies
7
Views
3K
High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Keisler Elementary Calculus: computing standard parts of expressions
  • · Replies 26 ·
Replies
26
Views
3K
Focussing a collimated beam using a diffraction grating
  • · Replies 1 ·
Replies
1
Views
949
Undergrad Optimization problem with multiple outputs: impossible?
  • · Replies 6 ·
Replies
6
Views
3K
Solve the differential equation: y′′y′+yy′+yy′′=0
  • · Replies 5 ·
Replies
5
Views
2K
Big Bang Nucleosynthesis; electron-photon ratio
  • · Replies 0 ·
Replies
0
Views
2K