number of real roots of the equation?

Question

number of real roots of the equation

$11^x+13^x+17^x-19^x=0$.

I don't remember similar questions done. Since this is not a polynomial equation.

score 4 · Accepted Answer · answered Mar 02 '20 at 16:34

4

HINT

Rewrite it as $$\left(\frac{11}{19}\right)^x+ \left(\frac{13}{19}\right)^x+ \left(\frac{17}{19}\right)^x=1$$

What can you say abou the function on the left-hand side?

answered Mar 02 '20 at 16:34

saulspatz

How do we get the solution $x\approx 3.87479$? – Luke Collins Mar 02 '20 at 16:48
@LukeCollins You have to do it numerically. Even bisection will work fast enough for this one, I would guess. – saulspatz Mar 02 '20 at 16:52
I misread, and thought the asker was after solutions, not number of solutions. – Luke Collins Mar 02 '20 at 16:53
@LukeCollins Oh I see. No problem. – saulspatz Mar 02 '20 at 16:56

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