4. If logza a = x, logza 2a = y, and log4a 3a = z, then xyz - 2yz is equal to (a) 1 (b)-1 (c)-2 (d) 2

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( begin{aligned} log _{2 a}^{a}=x &, log _{3 a}^{2 a}=y cdot log _{4 a}^{3 a}=z x y z=& log _{2 a}^{a} cdot log _{3 a}^{2 a} cdot log _{4 a}^{3 a} =& log _{4 a}^{a} 2 y z=& 2 log _{2 a}^{2 a} cdot log _{3 a}^{2 a} cdot log _{49}^{3 a} =& 2 log _{4 a}^{2 a} x y z-2 y z=& log _{4 a}^{a}-log _{4 a} 4 a^{2} &=log _{4 a}^{log _{4 a} x}=-log _{4 a}^{4 a}=-1 end{aligned} )

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