logarithm

(noun)

for a number $x$ , the power to which a given base number must be raised in order to obtain x; written logbx.; for example, log216 = 4 because 24 = 16

Related Terms

Examples of logarithm in the following topics:

  • pOH and Other p Scales

    • If we take the negative logarithm of each concentration, we get:
    • Quite often we will see the notation pKa or pKb, which refers to the negative logarithms of Ka or Kb, respectively.
    • Switch between logarithmic and linear scales.

  • Acid Dissociation Constant (Ka)

    • Due to the many orders of magnitude spanned by Ka values, a logarithmic measure of the acid dissociation constant is more commonly used in practice.
    • The logarithmic constant (pKa) is equal to -log10(Ka).

  • The Henderson-Hasselbalch Equation

    • With a given pH and known pKa, the solution of the Henderson-Hasselbalch equation gives the logarithm of a ratio which can be solved by performing the antilogarithm of pH/pK­a:

  • The Acid Dissociation Constant

    • Due to the many orders of magnitude spanned by Ka values, a logarithmic measure of the acid dissociation constant is more commonly used in practice.
    • The logarithmic constant, pKa, which is equal to −log10 (Ka), is sometimes incorrectly referred to as an acid dissociation constant as well.

  • Dilutions of Solutions

    • Serial dilutions are used to accurately create extremely diluted solutions, as well as solutions for experiments that require a concentration curve with an exponential or logarithmic scale.

  • Acid-Base Properties of Water

    • If we take the negative logarithm of both sides of this equation, we get the following:

  • Dating Using Radioactive Decay

    • Here, t is age of the sample; D is number of atoms of the daughter isotope in the sample; D0 is number of atoms of the daughter isotope in the original composition; N is number of atoms of the parent isotope in the sample at time t (the present), given by N(t) = Noe-λt; and λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2.

  • Calculating Equilibrium Concentrations of Polyprotic Acids

  • Half-Life

    • By rearranging this equation and using the properties of logarithms, we can find that, for a first order reaction:

  • The Importance of Conjugation

    • The spectrum of the unsaturated ketone (on the left) illustrates the advantage of a logarithmic display of molar absorptivity.