# CAT 2023 Set-3 | Quantitative Aptitude | Question: 4

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Q. 4)

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

1. $\log _{4}\left(\frac{23}{2}\right)$
2. $\log _{4}\left(\frac{3}{2}\right)$
3. $\log _{4} 7$
4. $\log _{4}\left(\frac{7}{2}\right)$

Q. 4)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...
Section: Quantitative AptitudeQ. 1)If $x$ is a positive real number such that $x^{8}+\left(\frac{1}{x}\right)^{8}=47$, then the value of $x^{9}+\left(\frac{1}{x}\right)^{... 0 votes 0 answers 3 55 views Q. 2)Let$n$and$m$be two positive integers such that there are exactly 41 integers greater than$8^{m}$and less than$8^{n}$, which can be expressed as powers of 2 . ... 0 votes 0 answers 4 55 views Q. 3)For some real numbers$a$and$b$, the system of equations$x+y=4$and$(a+5) x+\left(b^{2}-15\right) y=8 b$has infinitely many solutions for$x$and$y$. Then, the... 0 votes 0 answers 5 53 views Q. 5)A quadratic equation$x^{2}+b x+c=0$has two real roots. If the difference between the reciprocals of the roots is$\frac{1}{3}\$, and the sum of the reciprocals of t...