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8 Αυγ 2023 · Logarithms is a method to represent a significantly large mathematical value, and it helps to identify how many times a number has to be multiplied to get a desired other number. Logarithms are represented as a base number and power to that base number, using the equation logₕ a=y. Let’s understand logarithms using an example.
A negative log means that we will use a negative exponent (power) when we convert from log form to exponential form. Remember that a negative exponent means that we are dividing by a number rather than multiplying.
We're at the typical "logarithms in the real world" example: Richter scale and Decibel. The idea is to put events which can vary drastically (earthquakes) on a single scale with a small range (typically 1 to 10).
Then what do we mean by the negative logarithms? It means that the logarithm of the set of such numbers gives a negative result. All the numbers that lie between 0 and 1 have negative logarithms.
Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest).
6 Οκτ 2021 · Negative numbers and zero are not in the domain of the logarithm. At this point it may be useful to go back and review all of the rules of exponents. Example \(\PageIndex{2}\)
In chemistry, the acidity of a solution is measured in pH, which is defined as the negative logarithm of the concentration of hydrogen ions. This basically means that as pH increases by $1$, the concentration of hydrogen ions decreases tenfold, leading to a substantially less acidic solution in return.
