for what value of x is this possible
4^x + 6^x=9^x
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Since this is posted under "Number Theory" is x assumed to be a positive integer? If so, there is no such x. for all x> 1. since , there is a root between 1 and 2.
Hello, jashansinghal! For what value of is this possible? . We have: .
Divide by . . . . . We have a quadratic in
Quadratic Formula: .
Since , the only root is: . , the Golden Mean.
So we have: .
Take logs: .