CAT 2023 Logarithms Question (Hard)

Question

For a real number , if are in an arithmetic progression, then what is the common difference?

Accepted Answer

Step 1 Understand the given terms We are given that the following three terms are in Arithmetic Progression A.P. - First term - Second term - Third term So the three terms in A.P. are 2 , quad log_ 4 2 x - 9 , quad log_ 4 left 2 x 2 right --- Step 2 Apply A.P. condition In an arithmetic progression,

CAT 2023

Quantitative

Logarithms

Hard

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?

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