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, a vector which has zero magnitude is also a vector in case of two vectors travelling in opposite directions with equal magnitudes. At this case, the resultant vector has zero magnitude but it is still a vector. We call it a null vector.

Suicidal bag also known as lysosome is a cell organelle which are sphere shaped sacs filled with hydrolytic enzymes that have the capability to break down many types of biomolecules including the useful cells and materials that can derail the functioning of the cell . It mostly occurs in ageing, dead and diseased cells.

Lysosome is called as suicidal bag because it helps in the self-destruction of its cell, tissue or organs by releasing the lysosomal enzymes caused by rupturing of their...

If one could be a billionaire by following a how-to guide step by step, you'd have already come across it by now. 

Well, the how-to "BE" part is simple; own anything that's worth a billion- an idea, an asset, a skill, anything. It is the how-to reach that milestone that is mystic. Carve your own path to it. 

Once you find the secret (IF there is one), share it on Mattrab :P 

Or maybe don't ;) let others find their own path.