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Solve the equation 2x^(log(4)^(3))+3^(lo...

Solve the equation `2x^(log_(4)^(3))+3^(log_(4)^(x))=27`

Text Solution

Verified by Experts

The domain of the admissible value of the equation is `xgt0`. The given equation is equivalent to
`2.3^(log_(4)x)+3^(log_(4)^(x))=27` [from above result (v)]
`=3.3^(log_(4)^(x)=27`
`=3^(log_(4)x)=9`
`implies3^(log_(4)x)=3^(2)`
`implieslog_(4)x=2`
`impliesx_(1)=4^(2)=16` is its only root.
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