Solving an Exponential Diophantine Equation

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[misterdubity]

Note that 1984 in binary is which is 11 characters. This is the difference of minus The positive difference between 2 powers of 2 will always be, in binary, a string of 1s followed by a string of 0s

[MrGeorge]

First guess and away from pen and paper would be 2048 minus 64.

[weylguy]

A little better than guessing is to ignore the 2^y term, which gives x = 10.95. Rounding to x = 11, we than get y = 6.