


Logarithms
Logarithms were invented independently by John Napier(in 1614) and Joost Burgi(in 1620).The log is being useful in many fields from astronomy to common finance. We know multiplication is a helpful shortcut for adding,and the topic exponent is one of the shortcuts for multiplication,and log is the shortcut for exponents. Let "b" be a positive number b≠ 1.For any real number x, b^{x}x, then the exponent x is called the log of "a" to the base "b". We also call x, the value of log, log_{ b} a. Thus x = log_{b} a is an equivalent form of a= b^{x}. We say that x = log_{b} a is the logarithmic form of the exponential form a = b^{x}. In both forms the base is same. We observe that x = log_{b} a is an equivalent way of writing a = b^{x}. For example,
The Base must be specified in the logarithmic notation. If we write y = log x, then it will become meaningless, since its equivalent cannot be written unless the base is given. However, in such situations, we write logarithm, by omitting their base. In such case, it is understood that all logs are having the same base. Change the following logrithmic form into exponential form: (i) log_{25} 5 = 1/2Solution: 5=25^{1/2} (ii)log_{216} 6 = 1/3
(ii) 9^{3 = 1/729}. Evaluate: (iii) log_{9} 1/27
Solve the equations:


