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in Logarithms by (47.9k points)

Prove that : log4[log2{log2 (log3 81)}] = 0

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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.

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