ABC26GN2042 · Logarithms
Subject: General Aptitude · Chapter: Logarithms · Exam: · Marks: · Difficulty:
The value of $\log _{2}\left[\log _{2}\left\{\log _{4}\left(\log _{4} 256^{4}\right)\right\}\right]$ is
Answer
Explanation
$\log _{2}\left[\log _{2}\left\{\log _{4}\left(\log _{4} 256^{4}\right)\right\}\right]=\log _{2} \log _{2}\left[\log _{4}\left\{\log _{4}\left(4^{4}\right)^{4}\right\}\right]=$ $\log _{2} \log _{2}\left[\log _{4}\left\{\log _{4} 4^{16}\right\}\right]$ $=\log _{2} \log _{2}\left[\log _{4}\left\{16 \log _{4} 4\right\}\right]=\log _{2} \log _{2} \log _{4} 16=\log _{2} \log _{2}$ $\log _{4}\left(4^{2}\right)=\log _{2} \log _{2}\left(2 \log _{4} 4\right)$ $=\log _{2} \log _{2} 2=\log _{2} 1=0$.
Explanation as extracted from the printed page; notation may be imperfect.
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