Hint:
Express the RHS as ( (4^x - 2) + (2^x - 4) )^3
Expand as: (4^x - 2)^3 + (2^x - 4)^3 + 3(4^x - 2)^2(2^x - 4) + 3(4^x - 2)(2^x - 4)^2
Set this equal to the LHS and rearrange to get (4^x - 2)(2^x - 4)(4^x + 2^x - 6) = 0
I'll leave you to take it from here!
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