The order of magnitude of a physical quantity is its magnitude in powers of ten when the physical quantity is expressed in powers of ten with one digit to the left of the decimal.
Orders of magnitude are generally used to make very approximate comparisons and reflect very large differences.
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...
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.
Matter is anything that possesses mass, occupies space and may be perceived through one or more senses.
The physical divisions of matter are:
1. Solid : Solid matter is composed of tightly packed particles. A solid will retain its shape; the particles are not free to move around.
2. Liquid : Liquid matter is made of more loosely packed particles. It will take the shape of its container. Particles can...