Question

If x is the product of the logarithms of 2, 3, 4,......,10, which of the following will be true ?
1. x = 1
2. x < 1
3. x > 1
4. Can't say

Answer 1

Correct Answer - Option 2 : x < 1

Calculation :

We know that product of numbers that are less than 1 is always less than 1.

Also, logarithms of 2, 3, 4,.....,9 are less than 1 and log 10 = 1

As given, x = log 2 × log 3 × log 4 × log 5 × log 6 × log 7 × log 8 × log 9 × log 10 

So, x will always be less than 1.

When numbers less than 1 are multiplied by each other their multiplication will always be less than 1 and also less than each of those numbers.