Question

1)log₅√5+log₅5√5+1.25=
2)$frac{1}{3}$ log₂8 × log₂2 - 1=
3)log₃ $frac{1}{2}$ +log₃6=

Answer 1

$1); ; log_5sqrt5+log_5(5sqrt5)+1,25=log_55^{1/2}+log_55^{3/2}+1,25=\\=frac{1}{2}+frac{3}{2}+1,25=2+1,25=3,25\\2); ; frac{1}{3}cdot log_28cdot log_22-1=frac{1}{3}cdot log_22^3cdot 1-1=frac{1}{3}cdot 3-1=1-1=0\\3); ; log_3frac{1}{2}+log_36=log_32^{-1}+log_3(3cdot 2)=-log_32+log_33+log_32=\\=log_33=1$