[tex]log_{\sqrt{2}} \frac{\sqrt2}{2} [/tex]
[tex]log_5 \sqrt125[/tex]

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= -1log5 √125 = log5 √5³=log5 5^3/2 =3/2 log5 5=3/2