#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#
