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

← CAT 2023 Slot 3 QA

CAT 2023 Slot 3 QA · Question 1

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

A.
$lo g_{4} 7$
B.
$lo g_{4} (\frac{3}{2})$
C.
$lo g_{4} (\frac{7}{2})$
D.
$lo g_{4} (\frac{23}{2})$

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