If \log_2 [3+ \log_3 (4 + \log_4 (\x -1))] -2 = 0 then 4x equals

CAT Exam 2021 Slot 2 Solved Paper

Question : 54 of 66

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\log_2 [3+ \log_3 (4 + \log_4 (\x -1))] -2 = 0

then 4x equals

Solution:

We have

\log_2 [3+ \log_3 (4 + \log_4 (\x -1)] =2

We get

{\log_2} {3+ \log_3 (4 + \log_4 (\x -1))} =4

We get

\log_3 4 + \log_4 (\x - 1) =1

We get

4 + \log_4 (\x - 1) = 3

\log_4 (\x - 1) = -1

\x-1 = 4^{-1}

\x = 1/4 + 1 = 5/4

4\x = 5

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