Question

$log_{sqrt{2}} frac{sqrt2}{2}$
$log_5 sqrt125$

Answer 1

log √2   √2/2 = log 2^1/2  2^1/2*2^-1= log 2^1/2  2^-1/2 = 2*(-1/2) log2 2= -1
log5 √125 = log5 √5³=log5 5^3/2 =3/2 log5 5=3/2