Question

log9 √5 * log25 √3

Answer 1

$log_{9}sqrt{5}timeslog_{25}sqrt{3}=log_{3^{2}}5^{frac{1}{2}}timeslog_{5^{2}}3^{frac{1}{2}}=frac{1}{4}timeslog_{3}5timesfrac{1}{4}timeslog_{5}3=frac{1}{4}timesfrac{1}{4}times1=frac{1}{16}=0.0625=2^{-4}$

Answer 2

$log_{9} sqrt{5}*log _{25} sqrt{3}=log _{9} 5^{frac{1}{2}}*log _{25} 3^{frac{1}{2}}= frac{1}{4}*log _{9}5*log _{25}3= frac{1}{4}*log _{3} 5^{frac{1}{2}}*log _{5} 3^{frac{1}{2}}= frac{1}{16}log _{3}5*log _{5}3= frac{1}{16}*1= frac{1}{16}$