Solve: `log_axlog_a(xyz)=48`; `log_aylog_a(xyz)=12`; `log_azlog_a(xyz)=84`

Answer

`x=a^(4),y=a,z=a^(7)`

Explanation

Adding given equations
`log_(a)(xyz)[log_(a)x +log_(a)y+log_(a)z]=144`
`rArr log_(a)(xyz)=(144)^(1//2)=12`
`rArr xyz = a^(12)`
From `log_(a)x log_(a)(xyz)=48`
`rArr (log_(a)x)(12)=48`
`rArr log_(a)x=4`
`rArr =a^(4)`
Similary y = a and `z=a^(7)`