Cho a là số thực dương khác 1 . Mệnh đề nào dưới đây đúng? A. log_(sqrt [7](a))((1)/(a^9))=-(1)/(63) B. log_(sqrt [7](a))((1)/(a^9))=-63 C. log_(sqrt [7](a))((1)/(a^9))=63 D. log_(sqrt [7](a))((1)/(a^9))=(1)/(63)

To solve the problem, we need to determine which statement is true. <br /><br />The correct answer is D. $log_{7}\sqrt {a}(\frac {1}{a^{9}})=\frac {1}{63}$.<br /><br />Explanation:<br />We can rewrite the equation as $\frac{1}{63} = \log_{7}\sqrt{a}\left(\frac{1}{a^9}\right)$.<br /><br />Using logarithmic properties, we can simplify further:<br /><br />$\frac{1}{63} = \log_{7}\left(\frac{\sqrt{a}}{a^9}\right)$<br /><br />$\frac{1}{63} = \log_{7}\left(\frac{1}{a^{16}}\right)$<br /><br />$\frac{1}{63} = -\log_{7}(a^{16})$<br /><br />$\frac{1}{63} = -16\log_{7}(a)$<br /><br />Taking the reciprocal of both sides:<br /><br />$63 = -\frac{1}{16\log_{7}(a)}$<br /><br />$-\frac{1}{63} = \frac{1}{16\log_{7}(a)}$<br /><br />$\frac{1}{63} = -\frac{1}{16\log_{7}(a)}$<br /><br />Therefore, the correct statement is D. $log_{7}\sqrt {a}(\frac {1}{a^{9}})=\frac {1}{63}$.