Log2aa=x then, a=(2a)x ......(1)
Log3a2a=y then,2a=(3a)y ......(2)
Log4a 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.
It is theoretically possible for a substance to have a negative value of cubical expansivity, which means that the substance would contract rather than expand when the temperature increases. However, it is very rare for a substance to have a negative value of cubical expansivity over a significant range of temperatures.
One example of a substance that has a negative value of cubical expansivity over a limited range of temperatures is water. Water has a positive value of cubical expansivity at...