Question

$\frac{log \sqrt{8} }{log8} = ?$
Please answer with good solution !.

Answer 1

It can be written as :-
$log_{8} \sqrt{8} = log_{8} 8^{\frac{1}{2} }$
=$\frac{1}{2} log_{8}8$
=$\frac{1}{2}$.
Hence, found !

Answer 2

log√8/log8
[.·. √8= (8)^1/2 ]

=log (8)^1/2÷log (8)
[.·. 8= (2)^3 ]

=log (2)^3/2÷log (2)^3
(According, to log rule, the power comes down)
=3/2log(2)÷3log2
[log (2) gets cancelled]
=3/2÷3
=3/2×1/3
[3 gets cancelled]
Hence, answer is 1/2
log√8/log8=1/2