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(sqrt(ln(x)))/(ln sqrt(x))=6

You can square both sides of the equation that wil give you:

ln x/(ln^2x) = 6

Multiply both sides by the denominator

ln x = 6 ln^2 x

Subtract ln x from both sides which sets the equation equal to zero.

Factor by removing the greatest common factor of ln x. Then set both factors equal to zero and solve for x.

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