What is the application of the logarithm

Applications of the logarithm

Reading time: 6 min

We can discover logarithms in everyday life: For example, the pH value (measure of the acidic or basic character of an aqueous solution, see calculations below) and the decibel scale (measure of volume). Or just use it when it comes to your financial planning, as shown with compound interest.

Basically, logarithms are used where the values ​​are enormous.

Application example: pH value and logarithm

The pH value (abbreviation for Latin potentia hydrogenii = Ability of hydrogen) one considers concentrations between (acidic) and (alkaline) as a measure of the character of an aqueous solution. The scale to shows logarithmic values ​​according to the formula:

or in general with:

These are extremely small values ​​that can be better distinguished from one another using the logarithm.

We can rearrange the given formula as follows:

For example, vinegar has a pH of 2.5, which means:

As we can see, instead of just writing, we can write, which is much easier to read and memorize.

As we can see from the following table, the distinction is made easier by the ph values.

The minimum pH value is, that is, the indication of the concentration.
The maximum ph value is so.

Example for ph values

substancePH valueH+
Lemon juice

It is also interesting to know that our perception does not work linearly, but rather logarithmically. As with the decibel (unit for volume): We make a sound Not perceived twice as loud when its volume is doubled. No, you have to increase it many times over! Incidentally, the same applies to light. Doubled light (i.e. two light sources) does not produce light that is twice as bright for our perception.

Application example: Compare large numbers

If, for example, we are to determine whether is greater or less than, then our calculator has reached its limits because the numbers are far too large and do not fit in the memory. The logarithm provides a remedy here, with which we can carry out the comparison as follows:

This is how helpful the logarithm can be.