Bohr's theory of the atom was proposed in the early 20th century and was based on the idea that electrons move in fixed orbits around the nucleus. According to this theory, the position and momentum of an electron in an atom can be determined with absolute precision at any given moment, which seems to contradict Heisenberg's uncertainty principle.

Heisenberg's uncertainty principle states that it is impossible to determine the exact position and momentum of a particle simultaneously. This...

Time taken (t) = 3 sec
Velocity of sound (v) = 332 m/s
Distance travelled (d) = ?

We know,

d = v x t = 332 x 3 = 996 m

Hence, the source of thunder is about 996 m far from the boy.

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.