Functions {logarithmic function, exponential} can use variable powers of constant bases. ln(x) depends on base e {natural logarithm, base}. log(x) depends on base 10 {common logarithm}. Logarithms are exponential inverses.
Taking logarithm of value gives exponent to use with base. log(100) = x = log(10^x) = 2. ln(e^x) = x.
product
Product logarithm equals sum of factor logarithms {law of exponents}: log(M * N) = log(M) + log(N).
Exponential-function product equals exponential function of exponent sum: exp(x) * exp(y) = exp(x + y).
hyperbola
Logarithm equals area under hyperbola integrated from 1 to y, because hyperbola has equation y = 1/x, and integral of 1/y is logarithm.
line
Exponential equals 1 + n + n^2 / 2, for value n. Therefore, exponential equals 1 plus value plus area under line plus area under line at 45-degree angle.
Mathematical Sciences>Algebra>Function>Kinds>Exponential
3-Algebra-Function-Kinds-Exponential
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Date Modified: 2022.0224