2023 · Q33
Consider the following statements :
- 1log₁₀ 50 is a rational number.2. log₁₀₀ 10 is an irrational number.
Which of the statements given above is/are correct?
Elementary MathematicsAlgebra
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
If log₁₀50 = p/q were rational, then 10^(p/q) = 50 would give 2^p·5^p = 2^q·5^{2q}, forcing p = q and p = 2q simultaneously — impossible. So log₁₀50 is irrational. Meanwhile log₁₀₀1₀ = 1/2 since 100^{1/2} = 10, which is rational. Neither statement is correct (D).