Learn about logarithm and anti logarithm and some hidden tricks to solve these question easily.
What is Logarithm
Another way of writing the exponents is known as logarithm, in other words the logarithmic functions and exponentials are inverse of each other. Considering this inverse relationship between logarithmic functions and exponentials, one can successfully solve and graph logs just as a pie. To represent their inverse relationship in equation, we would write it as
However, it is necessary to keep in mind while writing log equation in exponential equation or exponential equation in log form that the base of exponent would be the same as the base of logarithm.
Finding the Logarithms
Due to the several helpful properties of logarithms scientists exceptionally implemented them to solve complex, lengthy calculations. For instance, in case they need to find out the product of two values x and y they an effortlessly find up by looking at both number’s log in the logarithmic table, then summing up their log and lastly again looking at the log table to find its antilogarithm (number that is written for the calculated log).
Thus we can say that to find the product of x and y we can simply add values written in the table for log x and log y. And then looking for the antilogarithmic value of that summed value in the table.
In the same manner, complex division problems can easily be solved by simply following the subtraction method with logs. For example, to divide x and y in log we would simply subtract log x from log y. Furthermore, logarithms can also help in simplifying the calculations of roots and powers.
While solving logarithms when according to the statement asking you to “expand," it means that the query contains one log expression with a lot of stuff inside it. And requires to use the log rules to break it down into several different log words, each with only one thing inside.
Thus when provided a single log with a complex argument and it needed to be changed into several logs, each with a specific argument.
For instance, you can use a log calculator. And get your answers in a single click.
What is Antilogarithm
Antilogarithm or simply he antilog as the name implies is the inverse of logarithm, in other words it is another name for exponents. However, we can define antilogarithm as when a base is raised to a power by log then the resultant number is called as the antilogarithm.
The process to find the antilog of a number is opposite to that of finding the log of that number. For instance, with a given base of a number y having its logarithm as x, then the antilogarithm of x having the base b should be y.
Finding the antilogarithm
An antilogarithmic table is used in order to find the antilog of a number however before finding out the antilogarithm of a number it is necessary to know about the mantissa part and characteristic part.
The characteristic part is the whole number part while the mantissa part is the decimal part of the logarithm number. The mantissa is always a positive value and in case a mantissa is given as a negative value it must be converted into positive value.
If the characteristic part of any whole number is positive in logarithm, then it is one less from the digits on the left side of the decimal point. In the process to find the antilog of a number the first step is to separate these characteristic and mantissa parts from each other forming the number value.
Then we have to find the corresponding value for the mantissa first by looking at the antilog table. To look for them in the table, the mantissa part’s first two digits are considered as row numbers while the column number is taken as for the third digit.
The columns that provide the mean difference are also present in the antilog table and find that mean difference for your value. However, the mean difference is equal to the column number for the same row of mantissa.
After noting down the values add all these values obtained and add one in the characteristic part. This value indicates where the decimal point should be placed. After so many digits to the left, the decimal point is added accordingly.
Antilog calculators can also help you to solve them in a second.
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