CAT 2023 Set-2 | Quantitative Aptitude | Question: 7

Question

For some positive real number $x$, if $\log _{\sqrt{3}}(x)+\frac{\log _{x}(25)}{\log _{x}(0.008)}=\frac{16}{3}$, then the value of $\log _{3}\left(3 x^{2}\right)$ is

Comments

Answer here!   

Answer 1

Here we need to apply basic logarithmic properties:

Comments

in $3rd$ line of solution. How we got from $\frac{2}{3}log_{0.2}5$ to $\frac{2}{3}*(-1)$

I think it can be re-written as $\frac{2}{3}log_{ \frac{2}{10}}5$ which is equal to $\frac{2}{3}log_{\frac{1}{5}}5$ which in turn is equal to $\frac{2}{3}log_{5^{-1}}5$ which finally gives us $\frac{2}{3}*(-1)$

Overall good solution