Compounds with hydrogen bonding tend to have higher melting and boiling points because the hydrogen bonding leads to stronger intermolecular forces. Intermolecular forces are the attractive forces between molecules, and they affect the physical properties of a substance, including melting and boiling points.

Hydrogen bonding is a particularly strong type of intermolecular force that occurs when a hydrogen atom is bonded to a highly electronegative atom such as nitrogen, oxygen, or fluorine....

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Yes, if the angle between the two vectors is more than 90^o but less than 270⁰. (cosΘ is negative)

In benzene molecule, carbon and carbon bond can't have polarity because there is not any electronegativity difference and the carbon hydrogen is also not much polar because the electronegativity difference is almost zero and also the small pull due to small difference in Electronegativity is balanced due to even pull from all directions.

In chlorobenzene the electronegativity difference between carbon and chlorine is very high so, it is polar.

(to compare polarity first check electronegativity...