0.3^(2+4+6+...+2x)>0.3^72

Question

0.3^(2+4+6+...+2x)>0.3^72

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Answer 1

0.3^{72}\\ 0.3^{\frac{2*2+2(x-1)}{2}*x}>0.3^{72}\\ (1+x)x>72\\ x+x^2>72\\ x^2+x-72>0\\ (x+9)(x-8)>0\\ ---------------->x\\ + \ \ \ (-9) \ \ \ \ \ \ \ - \ \ \ \ \ \ \ \ \ \ \ \ \ 8 \ +\\ (-oo;-9) \ U \ (8;+oo)" alt=" 0.3^{2+4+6+...+2x}>0.3^{72}\\ 0.3^{\frac{2*2+2(x-1)}{2}*x}>0.3^{72}\\ (1+x)x>72\\ x+x^2>72\\ x^2+x-72>0\\ (x+9)(x-8)>0\\ ---------------->x\\ + \ \ \ (-9) \ \ \ \ \ \ \ - \ \ \ \ \ \ \ \ \ \ \ \ \ 8 \ +\\ (-oo;-9) \ U \ (8;+oo)" align="absmiddle" class="latex-formula">