Logarithm of numbers greater than one – Integer Fraction (Mantissa)

Base ten logarithm of a number is the power to which 10 is raised to give that number e.g.

628000 = 6.28 x10⁵

628000 = 10^0.7980 x 10⁵

= 10^{0.7980+ 5}

= 10^5.7980

Log 628000 = 5.7980

          Integer Fraction (mantissa)

If a number is in its standard form, its power is its integer i.e. the integer of its logarithm e.g. log 7853 has integer 3 because 7853 = 7.853 x 10³

Examples: Use tables (log) to find the complete logarithm of the following numbers.

(a)  80030        (b) 8      (c) 135.80

(a)  80030    =             4.9033

(b)  8              =             0.9031

(c)   13580    =             2.1329