Question

log9 √5 * log25 √3

Answer 1

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

Answer 2

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