Q.1} 1/5 < log of 2 to the base 10 < 1/3.......................can u tell whether this is true or false?? when itried got the statement as false..................

Lets assume the statement is true.

log₁₀2> 1/5

log_xy > z implies that y > x^z

Therefore,

2 > 10^1/5

or 2⁵>(10^1/5)⁵  (raising both sides to power 5)

or, 32>10, which is correct.

Now consider the other inequality.

log₁₀2< 1/3

Again, log_xy > z implies that y > x^z

Therefore 2 < 10^1/3

or, 2³>(10^1/3)³ (raising both sides to power 3)

or, 8>10, which is not true.

Hence, log₁₀2> 1/5 is right, but  log₁₀2< 1/3 does not hold.

So 1/5 < log of 2 to the base 10 < 1/3 is False