SOLUTION: X^4 + 2^x = 89

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Question 1176860: X^4 + 2^x = 89
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

First, notice that x= 3 is the solution


    3^4 + 2^3 = 81 + 8 = 89.



Second, notice that the left side of the equation is MONOTONOCALLY increasing function of x.


It implies that the found value  x= 3 is a UNIQUE solution to the equation: there is NO other solutions.


ANSWER.     The unique solution to the given equation is   x= 3.