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For a real number x x x , if 1 2 , log ⁡ 4 ( x 2 − 9 ) log ⁡ 4 4 , and log ⁡ 4 ( x 2 + 17 2 ) log ⁡ 4 4 \frac{1}{2}, \frac{\log_4(x^2 - 9)}{\log_4 4},...

CAT Medium Logarithms MCQ

Question

For a real number

xx
, if
12,log⁡4(x2−9)log⁡44, and log⁡4(x2+172)log⁡44\frac{1}{2}, \frac{\log_4(x^2 - 9)}{\log_4 4}, \text{ and } \frac{\log_4\left(\frac{x^2 + 17}{2}\right)}{\log_4 4}
are in an arithmetic progression, then the common difference is:

Options

A.
log⁡47\log_4 7
B.
log⁡4(32)\log_4\left(\frac{3}{2}\right)
C.
log⁡4(72)\log_4\left(\frac{7}{2}\right)
D.
log⁡4(232)\log_4\left(\frac{23}{2}\right)
arithmetic progressionlogarithmic equationsalgebraic manipulationcat 2023

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