#Let a, b, c satisfies 2^a + 4^b = 2^c and 4^a + 2^b = 4^c then find minimum value of c

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craggy plover
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Let a, b, c satisfies 2^a + 4^b = 2^c and 4^a + 2^b = 4^c then find minimum value of c
Could I get a hint for this?

rich meteorBOT
craggy plover
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I have tried using AM-GM, forming a quadratic equation and making discriminant positive, factorization, didn't seem to work.