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Câu hỏi: Cho hàm số $f(x)={{5}^{x}}{{.8}^{2{{x}^{3}}}}$. Khẳng định nào sau đây là sai?
A. $f(x)\le 1\Leftrightarrow x.{{\log }_{2}}5+2{{x}^{3}}\le 0$
B. $f(x)\le 1\Leftrightarrow x+6{{x}^{3}}.{{\log }_{5}}2\le 0$
C. $f(x)\le 1\Leftrightarrow x.{{\log }_{5}}5+6{{x}^{3}}\le 0$
D. $f(x)\le 1\Leftrightarrow x.{{\log }_{2}}\sqrt{5}+{{x}^{3}}\le 0$
A. $f(x)\le 1\Leftrightarrow x.{{\log }_{2}}5+2{{x}^{3}}\le 0$
B. $f(x)\le 1\Leftrightarrow x+6{{x}^{3}}.{{\log }_{5}}2\le 0$
C. $f(x)\le 1\Leftrightarrow x.{{\log }_{5}}5+6{{x}^{3}}\le 0$
D. $f(x)\le 1\Leftrightarrow x.{{\log }_{2}}\sqrt{5}+{{x}^{3}}\le 0$
Ta có $f(x)\le 1\Leftrightarrow {{5}^{x}}{{.8}^{2{{x}^{3}}}}\le 1\Leftrightarrow {{\log }_{2}}({{5}^{x}}{{.8}^{2{{x}^{3}}}})\le 0$
$\Leftrightarrow {{\log }_{2}}{{5}^{x}}+{{\log }_{2}}{{8}^{2{{x}^{3}}}}\le 0\Leftrightarrow x{{\log }_{2}}5+6{{x}^{3}}\le 0$
Hoặc ${{\log }_{5}}({{5}^{x}}{{.8}^{2{{x}^{3}}}})\le 0\Leftrightarrow x+6{{x}^{3}}.lo{{g}_{5}}2\le 0$
$\Leftrightarrow {{\log }_{2}}{{5}^{x}}+{{\log }_{2}}{{8}^{2{{x}^{3}}}}\le 0\Leftrightarrow x{{\log }_{2}}5+6{{x}^{3}}\le 0$
Hoặc ${{\log }_{5}}({{5}^{x}}{{.8}^{2{{x}^{3}}}})\le 0\Leftrightarrow x+6{{x}^{3}}.lo{{g}_{5}}2\le 0$
Đáp án A.