Whate is the practical application of logarithm?

2 Answers
Jun 25, 2018

Shown below (more calculus inlined )

Explanation:

A practical application of logarithms regarding mechanics:

You can use logarithms for models for particular real life situations

For example take a particle of mass # m # with only a resistant force of #vm # Newtons acting on it, where #v # is the velocity at time #t #

Use #F = ma => F = m (dv)/(dt) #

#=> -vm = m (dv)/(dt) #

#=> -v = (dv)/(dt) #

#=> - int 1dt = int (dv)/ v #

#=> -t + c = log_e v #

Where hence this logarithmic solution can be an appropriate model in understanding of the motion the particle has

Jul 16, 2018

Turning multiplication or division into addition or subtraction.

Explanation:

In the days before electronic calculators people used tables of logarithms to the base 10 and tables of their inverses called "anti-logarithms" to compute complicated multiplication or division using only addition or subtraction.

Using the properties of logarithms:

Let #y = a xx b#

Then #log_10 y = log_10 a + log_10 b = c# (Say)

Now, #y = 10^c# (Called the anti-logarithm of #c#)

So, with tables of #log_10 t and 10^t# one can multiply using addition.

The same is true of division using subtraction.

For historical interest see: https://www.maa.org/press/periodicals/convergence/mathematical-treasure-babbage-s-tables-of-logarithms