## solve log equations with sq.rt

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
santaclaus
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Joined: Tue Mar 03, 2009 12:17 am
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### solve log equations with sq.rt

sq.rt (log base 3sq.rt.(x - log base 4 sq.rt (x))=1/2
so, I would start by simplifying what's inside the first square root
sq.rt (3 to some power =x and 4 to some power gives me x) and i'm stuck here b/c i can't really apply any log rules until I get x first? and then if I do know what x is, it's in the square root =1/2

stapel_eliz
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sq.rt (log base 3sq.rt.(x - log base 4 sq.rt (x))=1/2
Please review this article on formatting, and reply with clarification and / or correction. I think you mean the equation to be as follows, but I'm not sure...?

. . . . .$\sqrt{\log_3\left(\sqrt{x\, -\, \log_4\left(\sqrt{x}\right)}\right)}\, =\, \frac{1}{2}$

When you reply, please include a clear listing of your steps and reasoning. Thank you!