​if log(base 2a)a=x, log(base 3a)2a=y, log(base 4a)3a=z, then xyz-2yz is equal to

a)1
b)-1
c)-2
d)2

Dear Student,
Please find below the solution to the asked query:

We have:log2aa=xlog3a2a=ylog4a3a=zxyz=log2aa log3a2a log4a3aBy base change formula we have:logyx=logzxlogzy, we get:xyz=logcalogc2a.logc2alogc3a.logc3alogc4a=logcalogc4axyz=log4aa....i2yz=2log3a2a log4a3a=2logc2alogc3a.logc3alogc4a=2 logc2alogc4a2yz=2 log4a2a= log4a2a2....As logmn=nlogm2yz= log4a4a2....iii-ii, we getxyz-2yz=log4aa- log4a4a2=- log4a4a2-log4aa=-log4a4a2a  loga-logb=logab=-log4a4a=-1Hencexyz-2yz=-1....Optionb

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