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# Subtracting Two Logarithms that is Equal to 0?

TopLogarithm can be called as inverse of exponent (in case when base is ‘e’). Consider a number 'X’ whose base is 'n’ then Logarithm will be defined as exponent which is raised to ‘n’ to obtain actual number 'X'. When A = BC then this expression will be referred to Logarithm of 'A' is 'C' whose base is ‘B’.

Mathematically, it is expressed as C = log B (A). This expression can also be pronounced as
Log B (A), it is the Inverse Function of 'Bc' function.

Some common laws which are followed by logarithmic expressions are:
1) When number and base in logarithmic expression are same then result will be 1. For instance, in expression log c (C) both base and number on base are same that’s why result will be one that is log c (C) = 1

2) Log of one (‘1’) will always be 0 and log of 0 will always give ∞ whatever is the base. That is Log (1) = 0 and log (0) = ∞.
Logarithmic Functions can perform addition, subtraction, multiplication, division etc.

Subtraction of the logarithmic terms can be done as shown below:
Let’s consider two logarithmic functions as ‘log B (A)’ and ’log B (C)’,

Subtraction of these two functions will be Log B (A) - log B (C) = log B (A / C).
Let’s take following example to understand how to subtract logarithm expression:
Log 10 2 - log 10 1 = 0.3010 – 0 = 0.3010.

Let’s find subtracting two logarithms that is equal to 0. Result ‘0’ can be obtained only in one condition when number or matrix or logarithmic expressions are subtracted from similar parameter. Such as 1 – 1 or 2 – 2 gives zero. Let’s find out for the logarithmic expression
Since 2 – 2 = 0, this can be written as
Log 10 (2) – log 10 (2)= 0.3010 – 0.3010 = 0.