Here, f(x)=x² -6 logx-3=0

f(2)=4-6 log2-3=-0.806

f(3)=9-6 log3-3=3.1373

f(2).f(3)=-0.806*3.1373=-2.529422 which is negative.

Hence, the root lies between 2 and 3

c₀ =(2+3)/2=2.5

f(2.5)=6.25-6 log 2.5-3=0.8623

Now

n	a(-ve)	b(+ve)	cn	f(cn)
0	2	3	2.5	0.8623
1	2	2.5	2.25	-0.050595
2	2.25	2.5	2.375	0.38664
3	2.25	2.375	2.3125	0.1631658
4	2.25	2.3125	2.28125	0.05506
5	2.25	2.28125	2.265625	0.001925

From the table,

f(2.265625)=0.001928<10^-2

Therefore, the...

According to the Heisenberg Uncertainty Principle, it is impossible to determine the exact spin of an electron at any given moment. The Uncertainty Principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. Spin is a form of intrinsic angular momentum, which means it does not correspond to any specific position in space, and therefore cannot be measured precisely at the same time as its position.

However, while we...

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.

Water is a vital substance for life on Earth, and it plays numerous important biological roles in living organisms. Some of the key biological roles of water are:

1. Universal solvent: Water is an excellent solvent for many substances, both organic and inorganic. This means that it can dissolve and transport a wide range of nutrients and minerals necessary for the growth and survival of living organisms.

2. Medium for metabolic reactions: Many metabolic reactions in living organisms require water...

There is, for sure, effect of gravity on fire. We know for a fact that fires on Earth are "pointy" while those in zero-gravity are "round". This is because fire is simply glowing gas. Gas is matter and matter has weight. For a body to have weight, gravity must influence it in some way.