AP Common Difference Log Fractions

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

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