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Common Logarithmic Function or Common logarithm is the logarithm with base equal to 10. It is also known as the decimal logarithm because of its base. The common logarithm of x is denoted as log x. Example: log 100 = 2 (Since 102= 100).

So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.

Because we have a base 10 number system, it made sense to use base 10 logarithms. These are also n=known as common logs. Why do mathematicians use log for the natural logarithm, but scientists use it for the base 10 logarithm? The notation ?" always stands for whatever logarithm is being treated as the default one.

Log is the inverse operation to exponentiation, just as division is the inverse of multiplication and vice versa. In simple cases the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, as 10 to the power 3 is 1000 (1000 = 10 × 10 × 10 = 103); 10 is used as a factor three times.

If you know the values of logp for every prime, these can be used to determine the logarithm of any positive rational number just by using the rules log(ab)=bloga and log(ab)=log(a)+log(b). And if you don't remember what log(2) is, remember 210=1024?1000, therefore 10log(2)?3, or log(2)?0.3.

While the base of a common logarithm is 10, the base of a natural logarithm is the special number e. Although this looks like a variable, it represents a fixed irrational number approximately equal to 2.718281828459. (Like pi, it continues without a repeating pattern in its digits.)

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.