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.

a)When silver nitrate comes in contact with skin, it is reduced to white color metallic silver.In most cases, a black stain appears due to formation of finely divided silver which has black color.

The black color is due to the decomposition of the Ag+ ion into Ag, silver. Silver nitrate will slowly decompose with the silver ion reverting to elemental silver. The microscopic particles of silver are so small that they absorb light instead of reflecting it, and so appear black, instead of silver....