CAT 2023 Logarithms — Previous Year Question

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