#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#