2 votes 2 votes $\log _{2} x \times \log _{x/64}2 = \log _{x/16}2$ x=? Please provide elaborative answer. Quantitative Aptitude logarithms + – anupamsworld asked Jul 25, 2022 anupamsworld 385 views answer comment Share Follow See 1 comment See all 1 1 comment reply Kabir5454 commented Jul 26, 2022 i edited by Shaik Masthan Jul 26, 2022 reply Follow Share $\large \log_{2}x*\log_{\frac{x}{64}}2=\log_{\frac{x}{16}}2$ $\large \log_{2}x *\frac{\log_{2}2}{\log_{2}\frac{x}{64}}=\frac{\log_{2}2}{\log_{2}\frac{x}{16}}$ $\large \log_{2}x *\frac{1}{\log_{2}x-\log_{2}64}=\frac{1}{\log_{2}x-\log_{2}16}$ $\large \log_{2}x *\frac{1}{\log_{2}x-6}=\frac{1}{\log_{2}x-4}$ $\large \log_{2}x=\frac{\log_{2}x-6}{\log_{2}x-4}$ $\large (\log_{2}x)^{2}-5\log_{2}x+6=0$ $\large (\log_{2}x-3)(\log_{2}x-2)=0$ So, $\large (\log_{2}x-3)=0$ or $\large (\log_{2}x-2)=0$ So, $\large \log_{2}x=3$ or $\large \log_{2}x=2$ So,$\large x=8$ or $\large x=4$ 7 votes 7 votes Please log in or register to add a comment.