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Question

The value of 6+log32132 4132 41324132...... is

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Solution

Given that,

6+log32132 4132 41324132......(1)

Let us consider y= 4132(4132)4132

y=4132y

squaring on both sides

y2=4y32

32y2+y122=0

solving for y

y=1+1(4×32×122)2×32

y=1+28962=17162=1662

y=832

Substituting in (1)

6+log32[132×832]=6+log4932

=6log9432

=6log(32)232

=62log3232

=62

6+log32[132×832]=4

6+log32132 4132 41324132......=4

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