Expanding the Super Roots/Logs

Multiplication is iterative addition. Exponentiation is iterative multiplication. Tetration is iterative exponentiation. Pentation is iterative tetration. Etc. These are all hyperoperations and there are infinity many of them. But these are only one third of the bigger picture.

I want to know more about the logarithms and the radicals of these operations and how to compute them. There are such thing as super roots and super logarithms, but from what I know they only apply to tetration. Also, I have only really found a way of computing the super square root, but that is not enough for me! ssrt(x)=eW(lnx)=lnxW(lnx)      (W() denotes the product log and ssrt() denotes the super square root)\text{ssrt}(x) = e^{W(\ln x)} = \frac{\ln x}{W(\ln x)} \; \; \; \bigg( W(\cdot ) \text{ denotes the product log and ssrt}(\cdot) \text{ denotes the super square root} \bigg)

What I want to know is how you would write these expanded super roots/logs and if there is any way to compute them?

Note by James Watson
10 months, 1 week ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. 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 1

paragraph 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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

@Gandoff Tan

Yajat Shamji - 10 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...