Question

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

Answer 1

$1)\; \; log_5\sqrt5+log_5(5\sqrt5)+1,25=log_55^{1/2}+log_55^{3/2}+1,25=\\\\=\frac{1}{2}+\frac{3}{2}+1,25=2+1,25=3,25\\\\2)\; \; \frac{1}{3}\cdot log_28\cdot log_22-1=\frac{1}{3}\cdot log_22^3\cdot 1-1=\frac{1}{3}\cdot 3-1=1-1=0\\\\3)\; \; log_3\frac{1}{2}+log_36=log_32^{-1}+log_3(3\cdot 2)=-log_32+log_33+log_32=\\\\=log_33=1$