CATModern Math > Easy−log2(1/5)-\log _{2}(1 / 5)−log2(1/5)log2(1/5)\log _{2}(1 / 5)log2(1/5)−log2(1/3)-\log _{2}(1 / 3)−log2(1/3)log2(1/3)\log _{2}(1 / 3)log2(1/3)✅ Correct Option: 4Related questions:CAT 2021 Slot 1If 5−log101+x+4log101−x=log1011−x25-\log _{10} \sqrt{1+x}+4 \log _{10} \sqrt{1-x}=\log _{10} \frac{1}{\sqrt{1-x^{2}}}5−log101+x+4log101−x=log101−x21,then 100x100 \mathrm{x}100x equalsCAT 2019 Slot 1Let xxx and yyy be positive real numbers such that log5(x+y)+log5(x−y)=3\log _{5}(x+y)+\log _{5}(x-y)=3log5(x+y)+log5(x−y)=3, and log2y−log2x=1−log23\log _{2} y-\log _{2} x=1-\log _{2} 3log2y−log2x=1−log23. Then xyx yxy equalsCAT 2023 Slot 3For a real number xxx, if 12,log3(2x−9)log34\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}21,log34log3(2x−9), and log5(2x+172)log54\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}log54log5(2x+217) are in an arithmetic progression, then the common difference is