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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Physics
gptkb:signal_processing
gptkb:Probability_theory
gptkb:Acoustics
Chemistry
Engineering
Finance
Information theory
Computer science
Statistics
Complexity analysis
pH calculation
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gptkbp:basisFor
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b
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gptkbp:codomain
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All real numbers
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gptkbp:commonIn
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2
10
e
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gptkbp:continuity
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Yes
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gptkbp:designer
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gptkb:Exponential_function
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gptkbp:differentiable
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Yes
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gptkbp:domain
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x > 0
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gptkbp:field
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gptkb:Mathematics
gptkb:algebra
Analysis
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https://www.w3.org/2000/01/rdf-schema#label
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Logarithm function
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gptkbp:integration
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x*ln(x) - x + C
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gptkbp:inventedBy
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gptkb:John_Napier
Joost Bürgi
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gptkbp:monotonic
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Increasing
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gptkbp:notableDerivative
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1/x
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gptkbp:notation
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ln(x)
log(x)
log_b(x)
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gptkbp:property
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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)
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gptkbp:usedIn
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gptkb:Decibel
gptkb:Richter_scale
Fourier analysis
Entropy
Fractals
Algorithm analysis
Growth models
Logarithmic scale
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gptkbp:bfsParent
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gptkb:Entire_Functions
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gptkbp:bfsLayer
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7
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