(d) -1
\(x\) = log2a a = \(\frac{\text{log}\,a}{\text{log}\,2a}\), y = log3a 2a = \(\frac{\text{log}\,2a}{\text{log}\,3a}\)
z = log4a 3a = \(\frac{\text{log}\,3a}{\text{log}\,4a}\)
∴ xyz - 2yz = \(\frac{\text{log}\,a}{\text{log}\,2a}\).\(\frac{\text{log}\,2a}{\text{log}\,3a}\).\(\frac{\text{log}\,3a}{\text{log}\,4a}\) - 2\(\frac{\text{log}\,2a}{\text{log}\,3a}\).\(\frac{\text{log}\,3a}{\text{log}\,4a}\)
= \(\frac{\text{log}\,a}{\text{log}\,4a}\) - 2\(\frac{\text{log}\,2a}{\text{log}\,4a}\) = \(\frac{\text{log}\,a-2\,\text{log}\,2a}{\text{log}\,4a}\)
= \(\frac{\text{log}\,a-\,\text{log}\,(2a^2)}{\text{log}\,4a}\) = \(\frac{\text{log}\frac{a}{4}a^2}{\text{log}\,4a}\) = \(\frac{\text{log}\,(4a)^{-1}}{\text{log}\,(4a)}\) = \(\frac{-1.\text{log}\,4a}{\text{log}\,4a}\) = -1.