If $(\sqrt{2})^x+(\sqrt{3})^x=(\sqrt{13})^{x/2}$, then the number of real values of x is _____.

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We have, $(\sqrt{2})^x+(\sqrt{3})^x=(\sqrt{13})^{x/2}$ $⇒2^{x/2}+3^{x/2}=(\sqrt{13})^{x/2}$ $⇒(\frac{2}{\sqrt{13}})^{x/2}+(\frac{3}{\sqrt{13}})^{x/2}=(\frac{2}{\sqrt{13}})^{2}+(\frac{3}{\sqrt{13}})^2$ $⇒\frac{x}{2}=2$   [On comparison] $⇒x=4$