The logarithm is known as the inverse of the exponent function. It works opposite to that of exponent function. It tells us that to have a base we have to multiply. Log2 (x). Logarithm has a base, and the base is vertically lower. 

It is donated as logarithm In (x). Its rules are product rule, quotient rule, log of power, a log of e, a log of one, and a log of reciprocal. It has three types that are natural logarithm, binary logarithm, and common logarithm. Natural logarithm has e at its base, ‘e’ is a constant having the value of 2.718. It is used in physics and mathematics. It is simple and integrative. Binary logarithm, has 2 in its base. It is used in the computer sciences. These are the examples of the concave functions. Common logarithm has 10 at its base. It is used in astronomy, engineering, and biology. It functions as logarithmic function, inverse function, derivative and antiderivative, and integral representation of the natural logarithm.     

Pierre Simon Laplace called it as logarithm, a tool that is being used before computers and calculators have logarithms tables embedded in them. After Napier’s invention, Henry Briggs in 1617, compiled the first-ever table of the logarithm. 

Its advantages are that it is used in astronomy, engineering, photography, surveying, computer science, celestial navigation, mathematics, biology, economics, finding out the order of the magnitude, hardness of materials, brightness of stars, programming languages, logarithmic scale, music theory, physics, sound intensity, handheld calculators, chemistry, information theory, fractals, spectroscopy, and logarithmic graphs, and many more.

Antilogarithm is called an exponent. It is the reverse of the logarithm. To find an antilog firstly, decide what base you are going to find out. Most of the time the base is 10. Secondly, now find out what numbers antilog you are about to find. Thirdly, raise the base. And lastly, revise the process as well as the calculations. It is as log In. one should know about mantissa in the antilog as it is the fractional part of the common base 10.

One should know that antilog and natural log are different though their representation is the same. It can also be found using an inverse log calculator. It is the unzipping of the log function. It is used to model population growth and decline, compound interest, bacterial growth and decline, compound interest, spatial orientation, compute investments, and exponential decay.

  • To find out the logarithm, firstly, one should know the basic difference between the exponential and logarithmic equations. As for logarithm, Logarithmic: log ax = y and for exponent, Exponential: ay = x. Secondly, now know about all of the parts of the logarithm. Thirdly, what is the difference between the natural and common log? Fourth, now apply the properties of a logarithm known to you. Fifth, practice more and more by using the properties.
  • To find out the antilogarithm, firstly, know about the mantissa and the characteristics. Secondly, now use an antilog table to find out the values for your mantissa. Thirdly, now the value can be known from the mean difference columns. Fourth, now add up the values obtained. Fifth, now insert the decimal point.

In three steps, to find out antilog firstly, to know the value. Secondly, know the base. Thirdly, multiply by the base. For a logarithm, firstly, put the values in the log calculator. Secondly, apply alt + log than equals, you have your answer.

The difference between logarithm and antilogarithm is that logarithm tells us about the power of the base while the antilog applies that power to the base to have the number. Logarithm has to deal with the power while antilogarithm has to deal with the base.