![]() This is known as the binary system.ģ) Large numbers, like millions and billions, can be expressed very conveniently using log with the base 10. So, logarithms can be used to compute interest rates.Ģ) Logarithms with base 2 are used in computers. If $500 increase to $600 over a period of 5 years, log helps us calculate the rate of continuous return as: $$ rate = 0.036 = 3.6% $$ Hence, an interest rate of 3.6% is responsible for this change. It shows the effect of growing and the cause can be found using logarithms. Some examples are:ġ) Log can be used to model growth, like when a sum of money deposited in a bank increases over time. Logarithms are frequently used when dealing with large numbers. The idea of logarithms was proposed in the 17th century by Scottish mathematician, John Napier for ease of computations. The natural logarithm defines how many times e needs to be multiplied with itself to get 5. In this case, the logarithm is denoted by ln or log with e as the base. ![]() The other kind of logarithm is natural log, where the base is e, which is Euler’s number. For any other number, the base is always mentioned. For example, log 10 5 is simply written as log 5. For the common logarithm, if the base 10 is used, it is sometimes not explicitly mentioned, and is denoted only as log. ![]() In usual notations, the word ‘log’ denotes the common logarithm where the base is 10, although any base can be used. There are two types of logarithms: the common logarithm and natural logarithm. The log notation is a very convenient way of expressing large numbers. The logarithm can be calculated for only positive real numbers, and the base is a positive number not equal to 1. This basically shows that the number base ‘b’ must be raised to the power ‘y’ to obtain the value ‘x’. This is read as ‘the logarithm of x to the base b’. The corresponding log notation is y = log b x. The exponentiation is written as x = b y. For example, if ‘x’ is the number obtained when the base ‘b’ is raised to the power ‘y’, then the log operation will yield the number ‘y’, which is the power that the base ‘b’ must be raised to, in order to obtain ‘x’. This means that, the logarithm of a number is the power that the base must be raised to, to obtain this number. Logarithm (or log) is a mathematical operation which is the inverse of exponentiation.
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