Consider the following statements:<br>1. \log_{10}50 is a rational number.<br>2. \log_{100}10 is an irrational number.<br>Which of the statements given above is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 ✓
Correct Answer: D. Neither 1 nor 2
Explanation
Statement 1: \log_{10}50 = \log_{10}(100/2) = 2 - \log_{10}2, which is irrational. Statement 2: \log_{100}10 = \frac{1}{2}, which is a rational number. Therefore, neither statement is correct.
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?