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I solved it differently. I set a=5^x and b=2^x, substituted and got the following equation: a^2 (1-b) (1-2b) = 0, thus a^2 = 0 (no sol.) or 1-b=0 (x=0 -> false) or 1-2b=0 (x=-1, works), thus x=-1 :)
