Mathematics · Statistics
Binary-Log Ranking Discount rank plus one Solver
Rearrange the binary-log ranking discount relationship and solve for rank plus one.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use a=b^c with log2 rank discount=3.1699250014423126 and binary logarithm base two=2.
- rank plus one=9.000000000000002.
- Substitution into c=log_b(a) reconstructs 3.1699250014423126.
Understand Binary-Log Ranking Discount: solve rank plus one
One idea, three depths
Choose how deeply to explain Binary-Log Ranking Discount: solve rank plus one
Binary-Log Ranking Discount: solve rank plus one: Rearrange the binary-log ranking discount relationship and solve for rank plus one.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Binary-Log Ranking Discount: solve rank plus one to answer this question: rearrange the binary-log ranking discount relationship and solve for rank plus one? Enter log2 rank discount and binary logarithm base two; the calculator shows rank plus one. For example: rank plus one=9 and binary logarithm base two=2 produce log2 rank discount=3.1699250014423126. The answer tells you rank plus one.
Age 15Explain it to a 15-year-oldConnect it to the formula
A common DCG discount at rank r is log base two of r plus one. This page isolates rank plus one and verifies it in the original relationship. The rule is a=b^c. Its input values are log2 rank discount, binary logarithm base two, and the main result is rank plus one. For example: rank plus one=9 and binary logarithm base two=2 produce log2 rank discount=3.1699250014423126.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated binary-log ranking discount: solve rank plus one relation over the valid real-number domain stated below. The implemented relation is a=b^c, evaluated from log2 rank discount, binary logarithm base two to produce rank plus one. A common DCG discount at rank r is log base two of r plus one. This page isolates rank plus one and verifies it in the original relationship. Enter rank plus one, not the raw rank.
Inputs and valid domain
- log2 rank discount must be a finite real number.
- binary logarithm base two must be a finite real number.
Important boundary: Enter rank plus one, not the raw rank.
The formula
a=b^c
How the calculator works through it
It substitutes log2 rank discount, binary logarithm base two into the formula and exposes every numerical step above. The main output is rank plus one, accompanied by Reconstructed log2 rank discount.
Read the result correctly
The rank plus one is the direct answer to “rearrange the binary-log ranking discount relationship and solve for rank plus one.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
rank plus one=9 and binary logarithm base two=2 produce log2 rank discount=3.1699250014423126.
Where this model stops being reliable
Enter rank plus one, not the raw rank.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Binary-Log Ranking Discount: solve rank plus one works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Binary-Log Ranking Discount: solve rank plus one uses a=b^c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Binary-Log Ranking Discount: solve rank plus one inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Binary-Log Ranking Discount: solve rank plus one formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read log2 rank discount, binary logarithm base two.
- Evaluate the principal relationship: a=b^c.
- Return rank plus one and check the domain conditions described above.
Python
from math import *
def binary_log_rank_discount_solve_a(c, b) -> float:
return pow(b, c)
assert abs(binary_log_rank_discount_solve_a(3.1699250014423126, 2) - 9.000000000000002) < 1e-6 * max(1.0, abs(9.000000000000002))
C
#include <assert.h>
#include <math.h>
double binary_log_rank_discount_solve_a(double c, double b) {
return pow(b, c);
}
int main(void) {
const double expected = 9.000000000000002;
const double actual = binary_log_rank_discount_solve_a(3.1699250014423126, 2);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double binary_log_rank_discount_solve_a(double c, double b) {
return std::pow(b, c);
}
int main() {
constexpr double expected = 9.000000000000002;
const double actual = binary_log_rank_discount_solve_a(3.1699250014423126, 2);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double binary_log_rank_discount_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern pow
global binary_log_rank_discount_solve_a
section .text
binary_log_rank_discount_solve_a:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
movsd xmm1, [rbp-8]
call pow wrt ..plt
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = binary_log_rank_discount_solve_a(c, b)
result = (b ^ c);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, b_] := (b ^ c);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Binary-Log Ranking Discount rank plus one Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver
MLA 9
MW SysArc. “Binary-Log Ranking Discount rank plus one Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Binary-Log Ranking Discount rank plus one Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver.
Harvard
MW SysArc (2026) ‘Binary-Log Ranking Discount rank plus one Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_binary_log_rank_discount_solve_a_2026,
author = {{MW SysArc}},
title = {Binary-Log Ranking Discount rank plus one Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Binary-Log Ranking Discount rank plus one Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/binary-log-rank-discount-rank-plus-one-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Binary-Log Ranking Discount: solve rank plus one do?
Rearrange the binary-log ranking discount relationship and solve for rank plus one.
How does the Binary-Log Ranking Discount: solve rank plus one work?
The calculator applies a=b^c. A common DCG discount at rank r is log base two of r plus one. This page isolates rank plus one and verifies it in the original relationship.
What can I learn from the Binary-Log Ranking Discount: solve rank plus one?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .