2026 · Q8
Consider the following statements in respect of common logarithms :
- IThe logarithm of a number greater than 100 but less than 1000 lies between 2 and 3.
- IIThe logarithm of a positive number less than unity is negative.
Which of the statements given above is/are correct?
Elementary MathematicsAlgebra
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
For statement I, if 100 < N < 1000 then taking common logarithms gives 2 < log₁₀N < 3, so it is correct. For statement II, if 0 < x < 1 then log₁₀x < log₁₀1 = 0, so the logarithm is negative — also correct. Both statements are true, option C.