Question 1176860
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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.
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<U>ANSWER</U>.  &nbsp;&nbsp;&nbsp;&nbsp;The unique solution to the given equation is  &nbsp;&nbsp;x= 3.