Question

Log[log2{log2(log3 81)}]=0

Answer 1

log(log2(log2(log3 3⁴)))
=log(log2(log2(4log3 3)))
=log(log2(log2 4))
=log(log2(log2 2²))
=log(log2(2log2 2))
=log(log2 2)
=log 1
=0

Answer 2

The value of log(log2(log2(log3 81) is 0.

Given:

Th given logarithmic expression is log(log2(log2(log3 81).

To Find:

We need to find the value of the given logarithmic expression.

Solution:

We need to know some formulas of logarithms.

$log_{x} \ x^{m} =m$

$log_{x}\ x =1$

Using these formulas we will solve the problem.

$=log( log_{2}( log_{2} (log_{3}\ 81)))$

$=log( log_{2}( log_{2} (log_{3}\ 3^{4} )))$

$=log( log_{2}( log_{2} (4log_{3}\ 3)))$

$=log( log_{2}( log_{2} 4))$

$=log( log_{2}( log_{2} 2^{2} ))$

$=log( log_{2}( 2log_{2} 2))$

$=log( log_{2}2)$

$=log\ 1=0$

Therefore the value of the expression  $log( log_{2}( log_{2} (log_{3}\ 81)))$ is 0.

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