Olympiad Math Question | Solve Exponential Equation | Algebra Solutions Preparation 2022 2023

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mathsolympiad
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2^a+2^b =640
2^n<640 gives the maximum integer value for n =9 which gives 2^9 = 512
Substitute a= 9 in the given equation we get
512+2^b= 640
* 2^b = 640-512=128
2^b = 2^7
b= 7
The answer is a=9.b=7
N.Raja, Gobi

rajasengannann
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OMG... a and b are 7 and 9, respectively (or 9 and 7, respectively)... I solved it mentally by trial and error.

langleywallingford
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Well, a and b are obviously natural, otherwise the result wouldn't be natural.
640 = 512 + 128 = 2⁹ + 2⁷
⇒ a = 9, b = 7.

Nikioko