why we use base 10 in logirtham
Answers
Answer:
log with base 10 is used to simplify manual calculations and it is also related with decimal system. if we calculate log of any number with base 10, then integer just greater than that calculated value gives the no of digits in that number.
Historically logs to the base 10 were used for computation. Before calculators, textbooks in trigonometry and calculus included tables for log10 so that students could quickly compute products, quotients, powers, and roots. Usually it was a one-page table giving logs to four places. There were also log tables to five places in some textbooks. There was even a book of log tables to seven places.
We don’t use those tables anymore, so the main application of log10 is now obsolete.
There are a few places in science where log10 is used, primarily for logarithmic scales. Some examples are decibels for volume, Richter scale for earthquakes, entropy in thermodynamics, pH for acidity, and information in information theory.
Natural logs are important in mathematics since the derivative of logex is 1/x . That means that any part of mathematics that depends on calculus will need natural logs.
In calculus textbooks, logex is often written lnx , but in more advanced mathematics textbooks and mathematics research articles it’s usually just written logx .