log4270 means logarithm of 4270 to base 10.
Now we know that 10^0=1, 10=10^1, 100=10^2, 1000=10^3 and so on. Hence,
log1=0, log10=2, log100=2, log1000=3, log10000=4
As a number with one digit lies between 1 and 10, its log will be between 0 and 1
a number with two digits lies between 10 and 100, its log will be between 1 and 2
a number with three digits lies between 100 and 1000, its log will be between 2 and 3
a number with three digits lies between 1000 and 10000, its log will be between 3 and 4
and as 4270 lies between 1000 and 10000, it will be more than 3 but less than 4.
Here 3 i.e. number to the left of decimal "the whole number"part is called characteristic and is decided by number of digits in the given number. In fact, it is one less than number of digits.
But log4270 will be 3.----, and latter portion is called mantissa , the positive fractional part of logarithm. This number is available from logarithmic tables.
For 4270 it is 6304 and hence
log4270=3.6304
Note that for 427 it will be 2.6304
