The value of log2 log2 log4 256 + 2 log2 2 is

Question

The value of $\log_{2} \log_{2} \log_{4} 256 + 2 \log_{\sqrt{2}} 2$ is

Smart Achievers · Accepted Answer

(1)

$\log_{2} \log_{2} \log_{4} 256 + 2 \log_{\sqrt{2}} 2$

$= \log_{2} \log_{2} \log_{4} 4^{4} + \frac{2 \log 2}{\log \sqrt{2}}$ $[∵ \log_{x} x = 1]$

$= \log_{2} \log_{2} 4 + \frac{2 \log 2}{\frac{1}{2} \log 2}$

$= \log_{2} 2 + 4 = 1 + 4 = 5$

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