Υπολογιστής Logarithm
Χρησιμοποιήστε Υπολογιστής Logarithm για γρήγορα και ακριβή αποτελέσματα.
Πώς να χρησιμοποιήσετε αυτήν την αριθμομηχανή
- Εισαγάγετε Number
- Εισαγάγετε Base (optional, default 10)
- Κάντε κλικ στο κουμπί Υπολογισμός
- Διαβάστε το αποτέλεσμα που εμφανίζεται κάτω από την αριθμομηχανή
What Is a Logarithm?
A logarithm answers the question: "to what power must we raise a base to get this number?" Written as logb(x) = y, this means by = x. For example, log10(1000) = 3 because 103 = 1000.
The three most common types of logarithms are:
- Common logarithm (log₁₀ or simply log): base 10, used in pH calculations, decibels, and the Richter scale.
- Natural logarithm (ln): base e ≈ 2.71828, the foundation of calculus, exponential growth models, and statistics.
- Binary logarithm (log₂): base 2, used in computer science and information theory.
| x | log₁₀(x) | ln(x) = logₑ(x) | log₂(x) |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 0.3010 | 0.6931 | 1.000 |
| 10 | 1.000 | 2.3026 | 3.3219 |
| 100 | 2.000 | 4.6052 | 6.6439 |
| 1000 | 3.000 | 6.9078 | 9.9658 |
| e ≈ 2.718 | 0.4343 | 1.000 | 1.4427 |
Logarithms in Exercise Science and Data Analysis
Logarithms are essential in sports science, physiological research, and performance modeling. The VDOT tables developed by Jack Daniels use logarithmic relationships between race performance and oxygen cost. Heart rate variability (HRV), a key recovery metric for runners, is often analyzed using logarithmic-scale statistics (log-normal distribution).
The Borg RPE scale for perceived exertion follows a logarithmic progression. Training load metrics like ATL/CTL in popular platforms such as TrainingPeaks use exponential decay functions whose inverses are logarithms. Understanding log math helps you interpret these training tools more accurately.
In biochemistry, the pH scale used for sweat and blood analysis is logarithmic: each unit change in pH represents a 10-fold change in hydrogen ion concentration. Lactate threshold analysis in endurance sports also uses semi-log graphs.
Τελευταία ενημέρωση: March 2026
Frequently Asked Questions
What is the difference between log and ln?
log (without a base) typically means log base 10 (common logarithm). ln means the natural logarithm with base e ≈ 2.71828. They are related by: ln(x) = log(x) / log(e) ≈ log(x) × 2.3026.
Why is the natural logarithm called "natural"?
Because it arises naturally in calculus: the derivative of ln(x) is simply 1/x, making it the most mathematically elegant base for continuous growth and decay models. Population growth, radioactive decay, compound interest, and VO2 max decay during detraining all follow natural logarithmic relationships.
How do I change the base of a logarithm?
Use the change of base formula: logb(x) = log(x) / log(b) = ln(x) / ln(b). For example, log2(8) = log(8) / log(2) = 0.9031 / 0.3010 = 3.
What is log(0) or log of a negative number?
Logarithms are only defined for positive numbers. log(0) is negative infinity (undefined in practice), and log of a negative number is a complex number. Always check that inputs are positive before applying logarithms.