Question

1/2 log25/4base10-2log4/5base10+log320/125base10

Answer 1

Answer: 1

Explanation:

`\displaystyle\\(1)/(2)lg(25)/(4) -2lg(4)/(5) +lg(320)/(125)=\\\\lg\sqrt{(5^2)/(2^2) } -lg((4)/(5))^2+lg(5*64)/(5*25)=\\\\lg\sqrt{((5)/(2))^2 } -lg(4^2)/(5^2) +lg(64)/(25)=\\\\`

`lg(5)/(2) -lg(16)/(25)+lg(64)/(25) =\\\\ lg(5)/(2)+lg(64)/(25) -lg(16)/(25) =\\\\lg(5*64)/(2*25) -lg(16)/(25)=\\\\ lg(5*2*32)/(2*5*5)-lg(16)/(25)= \\\\lg(32)/(5)-lg(16)/(25)=\\\\lg(32*25)/(5*16)=\\\\lg(16*2*5*5)/(5*16) =\\\\lg(2*5)=\\\\lg10 =\\\\1`