The value of log_2(log_3(dots(log_{100}(100^{ | vedclass

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(B) Let the given expression be $E = \log_2(\log_3(\dots(\log_{100}(100^{99^{98^{\dots^{2^1}}})))\dots))}$.Using the property $\log_a(a^x) = x$,we sim

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$1$

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(B) Let the given expression be $E = \log_2(\log_3(\dots(\log_{100}(100^{99^{98^{\dots^{2^1}}})))\dots))}$.Using the property $\log_a(a^x) = x$,we simplify from the innermost logarithm:$\log_{100}(100^{99^{98^{\dots^{2^1}}}}) = 99^{98^{\dots^{2^1}}}$.Substituting this back,we get:$E = \log_2(\log_3(\dots(\log_{99}(99^{98^{\dots^{2^1}}})))\dots))$.Continuing this process,the expression simplifies step by step:$\log_{99}(99^{98^{\dots^{2^1}}}) = 98^{\dots^{2^1}}$.This pattern continues until we reach:$\log_3(3^{2^1}) = 2^1 = 2$.Finally,we have $E = \log_2(2) = 1$.

The value of $\log_2(\log_3(\dots(\log_{100}(100^{99^{98^{\dots^{2^1}}})))\dots))}$ is

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