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Find the value of $x$ $\frac{x^{\sqrt{x}}} {\sqrt{x}}=\frac{{\sqrt{x}}^x}{\sqrt{x}}$ Since both sides of the equation have a common denominator, multiply through by $\sq…

Find the integer solution for $3^x+27^y+81^z=10935$ This is a rather thickish question so we have to be very careful in our simplifications. The left hand side of the eq…

olve the logarithmic equations $\log_3(x+1)=\log_4(x+8)$ The bases of this equation is different so Let $\log_3(x+1)=y$...............................(i) And Let $\log_4…

How do you proof $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$? It is not always true. To see the clear picture, we solve some clear examples. Remember, $\sqrt{\frac{a}…

A Cool Infinite Series Yielding A Bunch of Known Constants Credits: gettyimages.com This is another beautiful proposition by Cornel Ioan Valean from Timi…