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 April 6th, 2017, 08:20 PM #1 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 exponential equation number of real solution of $\displaystyle 2017^x-2016^x = x$
 April 6th, 2017, 08:31 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,457 Thanks: 1338 $x=0,~x=1$ 2 real solutions Thanks from panky
 April 7th, 2017, 07:34 PM #3 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 Thanks romsek got it, $\displaystyle \displaystyle \frac{2017^x-2016^x}{2017-2016} = x$ Using LMVT , we have $\displaystyle f'(t) = x, f(t) = t^x\;, t \in \left[2016,2017\right]$ So $\displaystyle xt^{x-1} = x$. So we get $\displaystyle x=0\;, 1$

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