Question

evaluate the following without using log tables :-
log 9-log 3 by log27​

Answer 1

Answer:

1/3

Step-by-step explanation:

Logarithm laws:-

$log_{m}(a) log_{m}(b) = log_{m}( \frac{a}{b} ) \\ log_{m}( {a}^{x} ) = x log_{m}(a)$

$= log(9) - log(3) \div log(27) \\ = log( {3}^{2} ) - log(3) \div log( {3}^{3} ) \\ = 2 log(3) - log(3) \div 3 log(3) \\ = log(3) {(2 - 1)} \div 3 log(3) \\ >> cancelling \: log3 \\ = \frac{1}{3}$

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