Discussion
If logx(9/16) = -(1/2) then what is the value of x:
Answer: C
The value of x is 256/81.
Convert the logarithm to its exponential form:
\[ \begin{aligned} \log_x \tfrac{9}{16} &= -\tfrac{1}{2} \\ x^{-1/2} &= \tfrac{9}{16} \\ x^{1/2} &= \tfrac{16}{9} \\ x &= \left(\tfrac{16}{9}\right)^{2} = \tfrac{256}{81} \end{aligned} \]
The base of a logarithm must be positive, so \(-3/4\) and \(-256/81\) are impossible. 4/3 is the square root of the answer, what you get by stopping one step early with the square root instead of squaring.
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