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If \( \Large x^{x\sqrt{x}}= \left(x\sqrt{x}\right)^{x} \) , the x equals
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A) \( \Large \frac{4}{9} \) |
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B) \( \Large \frac{2}{3} \) |
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C) \( \Large \frac{9}{4} \) |
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D) \( \Large \frac{3}{2} \) |
Correct Answer:
| C) \( \Large \frac{9}{4} \) |
Description for Correct answer:
\( \Large x^{x\sqrt{x}} = \left(x\sqrt{x}\right)^{x} \)
\( \Large x^{x\sqrt{x}} = \left(x^{\frac{3}{2}}\right)^{x} \)
\( \Large 3^{x\sqrt{x}} = x^{\frac{3}{2}x} \)
\( \Large \left[ If\ bases\ are\ same\ then\ power\ are\ equal \right] \)
Therefore, \( \Large x\sqrt{x} = \frac{3}{2}x\ or\ \sqrt{x} = \frac{3}{2} \)
\( \Large x = \left(\frac{3}{2}\right)^{2} = \frac{9}{4} \)
\( \Large x^{x\sqrt{x}} = \left(x\sqrt{x}\right)^{x} \)
\( \Large x^{x\sqrt{x}} = \left(x^{\frac{3}{2}}\right)^{x} \)
\( \Large 3^{x\sqrt{x}} = x^{\frac{3}{2}x} \)
\( \Large \left[ If\ bases\ are\ same\ then\ power\ are\ equal \right] \)
Therefore, \( \Large x\sqrt{x} = \frac{3}{2}x\ or\ \sqrt{x} = \frac{3}{2} \)
\( \Large x = \left(\frac{3}{2}\right)^{2} = \frac{9}{4} \)
Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics
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