We know that logm mn = n logmm
and logmm = 1
∴ logm(m)n = n x logmm = n x 1 = n
⇒ logm(m)n = n …(i)
L.H.S. = log4[log2{log2(log3 81)}]
= log4[log2 {log2(log334)}] (∵ 81 = 34)
= log4[log2 {(log24)} [According to equal (i)]
= log4{log2(log222)} (∵ 4 = 22)
= log4(log22) [According to equal (i)]
= log4(1) (∵ logmm = 1)
= 0 = R.H.S.