<s>[INST] $2^x + 3^x - 4^x + 6^x - 9^x ≤ 1$ $\forall x \in R$ How can i prove that $2^x + 3^x - 4^x + 6^x - 9^x ≤ 1$ $\forall x \in R$.
I tried $log(2^x + 3^x - 4^x + 6^x - 9^x) = log (1296^x) = x log(1296)$ i don't know if im correct  here i stuck some help please
 [/INST] Note that
$$9^x-6^x+4^x-3^x-2^x+1=\frac{1}{2}\left(( 3^x-1)^2+(2^x-1)^2+(3^x-2^x)^2\right)>0$$
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