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 Calculus Calculus Math Forum

 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: 2,549 Thanks: 1399 $x=0,~x=1$ 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 $\displaystyle x=0\;, 1$ Tags equation, exponential Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Krvila4n9k Number Theory 10 September 29th, 2015 12:06 PM tva_vlad Calculus 3 January 4th, 2014 07:58 AM panky Calculus 2 September 19th, 2013 01:56 AM Silkenos Algebra 1 December 5th, 2010 07:50 PM tva_vlad Algebra 2 December 31st, 1969 04:00 PM

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