Whate is the practical application of logarithm?

Question

Benjamin Achtenberg · Accepted Answer

Shown below (more calculus inlined )

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

Christian Antunez · Answer

Turning multiplication or division into addition or subtraction.

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://tutor.hix.ai