Question

find the value of log 1/2 to the base 8

Answer 1

Hey user

Here is your answer :-

$let \: log_{8}( \frac{1}{2} ) = x \\ \\ by \: the \: defination \\ \\ {8}^{x} = \frac{1}{2} \\ \\ ({ {2}^{3} })^{x} = {2}^{ - 1} \\ \\ {2}^{3x} = {2}^{ - 1} \\ \\ 3x = - 1 \\ \\ x = \frac{ - 1}{3} \\ \\ so \: log_{8}( \frac{1}{2} ) = \frac{ - 1}{3}$
Thank you.