Google
Câu hỏi: Cho số thực x thỏa mãn $\log \text{x}=\dfrac{1}{2}\log 3\text{x}-2\log b+3\log \sqrt{c}$ (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: $VP=\dfrac{1}{2}\log 3\text{x}-2\log b+3\log \sqrt{c}=\log \sqrt{3\text{a}}-\log {{b}^{2}}+\log \sqrt{{{c}^{3}}}$
$=\log \dfrac{\sqrt{3\text{a}}.\sqrt{{{c}^{3}}}}{{{b}^{2}}}=\log \dfrac{\sqrt{3\text{a}{{c}^{3}}}}{{{b}^{2}}}$
Vậy $\log \text{x}=\log \dfrac{\sqrt{3\text{a}{{\text{c}}^{3}}}}{{{b}^{2}}}\Leftrightarrow x=\dfrac{\sqrt{3\text{a}{{c}^{3}}}}{{{b}^{2}}}$.
$=\log \dfrac{\sqrt{3\text{a}}.\sqrt{{{c}^{3}}}}{{{b}^{2}}}=\log \dfrac{\sqrt{3\text{a}{{c}^{3}}}}{{{b}^{2}}}$
Vậy $\log \text{x}=\log \dfrac{\sqrt{3\text{a}{{\text{c}}^{3}}}}{{{b}^{2}}}\Leftrightarrow x=\dfrac{\sqrt{3\text{a}{{c}^{3}}}}{{{b}^{2}}}$.
Đáp án D.