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Solve the equation 2log2x=log(7x-2-2x^...

Solve the equation
`2log2x=log(7x-2-2x^(2))`

Text Solution

Verified by Experts

This equation equivalent to the system
`{(2xgt0),((2x)^(2)=7x-2-2x^(2)):}`
`implies{(xgt0),(6x^(2)-7x+2=0):}`
`implies{(xgt0),((x-1//2))(x-2//3)=0):}`
`implies{(x=1//2),(x=2//3):}`
Hence`x_(1)=1//2` and `x_(2)=2//3` are the roots of the original equation.
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