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If log[10]x-log[10]sqrtx=2logx10, then p...

If `log_[10]x-log_[10]sqrtx=2log_x10`, then possible value of x is given by

Text Solution

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`log_10x-log_10sqrtx = 2log_x10`
`=>log_10(x/sqrtx) = 2/log_10x`
`=>log_10(x)^(1/2) = 2/log_10x`
`=>1/2log_10x = 2/log_10x`
`=>(log_10x)^2 = 4`
`=>log_10x = 2`
`=>x = 10^2 = 100`
`:. x = 100`
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