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log^2(100x)+log^2(10x)=14+log(1/x)...

`log^2(100x)+log^2(10x)=14+log(1/x)`

Text Solution

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`log^2(100x)+log^2(10x) = 14+log(1/x)`
`=>log(100x)^2+log(10x)^2 = 14-logx`
`=>(log100+logx)^2+(log10+logx)^2 = 14-logx`
`=>(2+logx)^2+(1+logx)^2 = 14-logx`
Let, `logx = t`, then our equation becomes,
`(2+t)^2+(1+t)^2 = 14 - t`
`=>4+t^2+4t+1+t^2+2t+t - 14 = 0`
`=>2t^2+7t-9 = 0`
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