Which of the following statements is/are correct?

I. If $2^x = 3^y = 6^{-z}$ , then $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$
II. $(243)^{0.16} \times (9)^{0.1} = 0.3$
III. If $3.105 \times 10^P = 0.00239 + 0.000715$ , then P = -3

Question

Which of the following statements is/are correct?

I. If

2^x = 3^y = 6^{-z}

, then

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0

II.

(243)^{0.16} \times (9)^{0.1} = 0.3

III. If

3.105 \times 10^P = 0.00239 + 0.000715

, then P = -3

Accepted Answer

D - I and III only. I: let 2^x = 3^y = 6^-z = k; then 1/x + 1/y + 1/z = (ln2 + ln3 - ln6)/lnk = 0, so I is true. II: 243^0.16 x 9^0.1 = 3^0.8 x 3^0.2 = 3, not 0.3, so II is false. III: 0.00239 + 0.000715 = 0.003105 = 3.105 x 10^-3, so P = -3 and III is true. Hence I and III only.

Answer

A - II only

Answer

B - II and III only

Answer

C - I and II only

Which of the following statements is/are correct? I. If \(2^x = 3^y = 6^{-z}\), then \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0\) II. \((243)^{0.16} \times (9)^{0.1} = 0.3\) III. If \(3.105…

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