Question

log raiz de 2 na base 8

Answer 1

$log_8 \sqrt{2}=x\\ \\ 8^x= \sqrt{2}\\ \\ 2^{3x} =2^{\frac{1}{2}}\\ \\ 3x=\frac{1}{2}\\ \\ x=\frac{1}{6}$

Answer 2

$log_{8} \sqrt{2} =log_{8} 2^{ \frac{1}{2} } = \dfrac{1}{2}. log_{8} 2= \dfrac{1}{2} . \dfrac{log_{2} 2}{log_{2} 8} = \dfrac{1}{2} . \dfrac{1}{log_{2} 2^{3} } = \dfrac{1}{2} . \dfrac{1}{3.log_{2} 2 }$$= \dfrac{1}{2} . \dfrac{1}{3.1} = \dfrac{1}{6}$