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Here it is given that the equation $11^x+13^x+17^x-19^x=0$ has only one real root. How can I show it? Please someone give some hints..

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Hint: $\;\;\displaystyle \left(\frac{11}{19}\right)^x+\left(\frac{13}{19}\right)^x+\left(\frac{17}{19}\right)^x\;$ is strictly decreasing, thus injective.

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