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CAT 2023 Set-3 | Quantitative Aptitude | Question: 4

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For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and $\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$ are in an arithmetic progression, then the common difference is

  1. $\log _{4}\left(\frac{23}{2}\right)$
  2. $\log _{4}\left(\frac{3}{2}\right)$
  3. $\log _{4} 7$
  4. $\log _{4}\left(\frac{7}{2}\right)$

     

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