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27 Αυγ 2020 · A logarithm is the answer to the question what power x do I need to apply to the base b in order to obtain the number y: log_b(y) = x is another way of specifying the relationship: b^x = y. Let’s plug in some numbers to make this more clear. We will do base-10, so b=10. log_10(100) = 2 The base-10 logarithm of 100 is 2 because: 10^2 = 100
It is because exponential functions are one-to-one. Whether you want to use logarithms or not they exist because a bijective function has an inverse. Logarithms put numbers on a human-friendly scale, such as the Richter scale, the Decibel scale, etc...
2 Μαΐ 2024 · Revision notes on Logarithmic Functions for the CIE IGCSE Additional Maths syllabus, written by the Additional Maths experts at Save My Exams.
In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. We write it like this: So these two things are the same:
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).
A logarithm can have any positive value (other than 1) as its base, but logs with two particular bases are generally regarded as being more useful than the others: the "common" log with a base of 10, and the "natural" log with a base of the number e.
We can calculate logs using the properties of logarithms. i.e., using the rules of logs we can either compress a set of logarithms into one or expand one logarithm as many. We also use log table and antilog table in calculations.
