Statements (47)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical Function
|
| gptkbp:application |
gptkb:Signal_Processing
gptkb:Physics gptkb:Complex_Analysis gptkb:Information_Theory Chemistry Computer Science Economics Biology Statistics |
| gptkbp:asymptote |
y-axis (x=0)
|
| gptkbp:basisFor |
b > 0, b ≠ 1
|
| gptkbp:codomain |
All real numbers
|
| gptkbp:concavity |
Concave down
|
| gptkbp:continuity |
Yes
|
| gptkbp:decreasing |
If 0 < b < 1
|
| gptkbp:designer |
gptkb:Exponential_Function
|
| gptkbp:differentiable |
Yes
|
| gptkbp:domain |
x > 0
|
| gptkbp:field |
gptkb:Mathematics
gptkb:algebra |
| gptkbp:graphics |
Passes through (1,0)
|
| gptkbp:hasSpecialCase |
Common Logarithm
Natural Logarithm |
| https://www.w3.org/2000/01/rdf-schema#label |
Logarithmic Function
|
| gptkbp:increasing |
If b > 1
|
| gptkbp:introducedIn |
17th century
|
| gptkbp:inventedBy |
gptkb:John_Napier
|
| gptkbp:monotonic |
Yes
|
| gptkbp:notation |
ln(x)
log(x) log_b(x) |
| gptkbp:property |
log_b(1) = 0
log_b(b) = 1 log_b(x) = ln(x)/ln(b) log_b(x/y) = log_b(x) - log_b(y) log_b(x^k) = k*log_b(x) log_b(xy) = log_b(x) + log_b(y) |
| gptkbp:range |
(-∞, ∞)
|
| gptkbp:usedFor |
Algorithm complexity (Big O notation)
Information entropy Measuring sound intensity (decibels) Richter scale for earthquakes Solving exponential equations pH scale in chemistry |
| gptkbp:bfsParent |
gptkb:Exponential_Function
|
| gptkbp:bfsLayer |
7
|