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Câu hỏi: . Cho số thực x thỏa mãn : $\log x=\dfrac{1}{2}\log 3a-2\log b+3\log \sqrt{c}$ ( $a,b,c$ là các số thực dương). Hãy biểu diễn x theo $a,b,c$.
A. $x=\dfrac{{{c}^{3}}\sqrt{3a}}{{{b}^{2}}}$
B. $x=\dfrac{\sqrt{3a}}{{{b}^{2}}{{c}^{3}}}$
C. $x=\dfrac{\sqrt{3ac}}{{{b}^{2}}}$
D. $x=\dfrac{\sqrt{3a{{c}^{3}}}}{{{b}^{2}}}$
A. $x=\dfrac{{{c}^{3}}\sqrt{3a}}{{{b}^{2}}}$
B. $x=\dfrac{\sqrt{3a}}{{{b}^{2}}{{c}^{3}}}$
C. $x=\dfrac{\sqrt{3ac}}{{{b}^{2}}}$
D. $x=\dfrac{\sqrt{3a{{c}^{3}}}}{{{b}^{2}}}$
Ta có: $\log x=\dfrac{1}{2}\log 3a-2\log b+3\log \sqrt{c}\Leftrightarrow \log x=\log \sqrt{3a}-\log {{b}^{2}}+\log \sqrt{{{c}^{3}}}$
$\Leftrightarrow \log x=\log \dfrac{\sqrt{3a}.\sqrt{{{c}^{3}}}}{{{b}^{2}}}\Leftrightarrow x=\dfrac{\sqrt{3a{{c}^{3}}}}{{{b}^{2}}}$.
$\Leftrightarrow \log x=\log \dfrac{\sqrt{3a}.\sqrt{{{c}^{3}}}}{{{b}^{2}}}\Leftrightarrow x=\dfrac{\sqrt{3a{{c}^{3}}}}{{{b}^{2}}}$.
Đáp án D.