Suppose that \(\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0\) then the value of \(a + b + c\) is

Question and options

Suppose that

\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0

then the value of

a + b + c

Correct answer: C - 89

log3(log4 a)=1 -> log4 a=3 -> a=64; log4(log2 b)=1 -> log2 b=4 -> b=16; log2(log3 c)=1 -> log3 c=2 -> c=9. Sum = 64+16+9 = 89.