Question

Evaluate the following without using log tables:-
log 27 by log √3​

Answer 1

Answer:

check the attachment

Step-by-step explanation:

first write 27 in power of 3, and √3 in the power of 3 as shown on the attachment.

Answer 2

Answer:

6

Step-by-step explanation:

27 = 3^3

Logarithm laws:-

$log_{a}( {m}^{x} ) = x log_{a}(m)$

$= \frac{ log(27) }{ log( \sqrt{3} ) } \\ = \frac{ log( {3}^{3} ) }{ log( {3}^{ \frac{1}{2} } ) } \\ = \frac{3 log(3) }{ \frac{1}{2} log(3) } \\ cancelling \: log3 \\ = \frac{3}{ \frac{1}{2} } \\ = \frac{3 \times 2}{1} = 6$