Notice that you may write 2.7=27/10, hence log 2.7 = log (27/10)

You need to remember the quotient property of logarithms, thus you should conver the logarithm log (27/10) in a difference of two logarithms such that:

log (27/10) = log 27 - log 10

You need to remember that log 10 = 1, hence log (27/10) = log 27 - 1

You may write 27 = 3^3 => log 27 = log 3^3 => log 27 = 3*log 3

You may use tables of common logarithms (base 10) for 1 to 10 to find log 3 = 0.477.

**log 2.7 = 3*0.477 - 1 = 0.431**

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