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Solve the following equation of x :2(log...

Solve the following equation of `x :2(log)_x a+(log)_(a x)a+3(log)_(a^2x)a=0,a >0`

Text Solution

Verified by Experts

The correct Answer is:
`x=a^(-1//2)or a^(-4//3)`
The given equation can be rewritten as
`(12)/(log_(a)x)+(1)/(log_(a)ax)+(3)/(log_(a)x)=0`
`implies1/t+(1)/(1+t)+(3)/(2+t)=0, where t =log_(a)x`
`implies2(1+t)(2+t)+3t(1+t)+t(2+t)=0`
`implies6t^(2)+11t+4=0`
`implies(2t+1)(3t+4)=0`
`impliest=-1/2or log_(a)x=-4/3`
`impliesx=a^(-1//2)`
`or x=a^(-4//3)`
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