When we extend this to the natural logarithm, we have, since e 0 = 1 ⇒ ln 1 = 0. Obviously, when a = 10, log 10 1 = 0 (or) simply log 1 = 0. Converting this into log form, log a 1 = 0, for any 'a'. Because from the properties of exponents, we know that, a 0 = 1, for any 'a'. The value of log 1 irrespective of the base is 0. Let us see each of these rules one by one here. If you want to see how all these rules are derived, click here. Here are the rules (or) properties of logs. The rules of logs are used to simplify a logarithm, expand a logarithm, or compress a group of logarithms into a single logarithm. Observe that we have not written 10 as the base in these examples, because that's obvious. In other words, it is a common logarithm. I.e., if there is no base for a log it means that its log 10. But usually, writing "log" is sufficient instead of writing log 10. i.e.,Ĭommon logarithm is nothing but log with base 10. But it is not usually represented as log e. Natural logarithm is nothing but log with base e. These two logs have specific importance and specific names in logarithms. Observe the last two rows of the above table. Here is a table to understand the conversions from one form to the other form.
This is called " log to exponential form" This is called " exponential to log form" The above equation has two things to understand (from the symbol ⇔): b, which is at the bottom of the log is called the "base".a, which is inside the log is called the "argument".Notice that 'b' is the base both on the left and right sides of the implies symbol and in the log form see that the base b and the exponent x don't stay on the same side of the equation. The right side part of the arrow is read to be "Logarithm of a to the base b is equal to x".Ī very simple way to remember this is "base stays as the base in both forms" and "base doesn't stay with the exponent in log form". A logarithm is defined using an exponent.
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