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Increasing and decreasing sides (Posted on 2024-10-17)

For a real number x, how many solutions does the equation 4^x + 7^x + 8^x + 10^x + 14^x + 15^x = 17^x + 19^x have?

No Solution Yet Submitted by Danish Ahmed Khan

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Am I missing something?

Comment 2 of 2 |

If we move all terms of the given equation to the LHS and set that equal to zero, it can be shown that that for x<0 the function is always >0 and has a limit of 0 for x-> -infinity. For x>=0, I believe there is only 1 real root, equal to 2.

Posted by Kenny M on 2024-10-17 10:11:54

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