Question

find (2 log6 +6log2)/(4log2+log27-log9)

Answer 1

hi friend,

firstly 2 log6 +6log2

→log6²+log2^6

→log36+log 64

→log 36×64

→log2304

now, 4log2+log27-log9

→log 16+log27-log9

→log 16(27)/9

→log 48

now, (2 log6 +6log2)/(4log2+log27-log9)

→log2304/log48

→log 48²/log48

→2

I hope this will help u :)

Answer 2

Given : 2 log6 +6log2)/(4log2+log27-log9)

To Find : Value

Solution:

2 log6 +6log2)/(4log2+log27-log9)

=2 log(3x2) +6log2)/(4log2+log27-log9)

using log(ab) = log a + logb

log a - log b = log (a/b)

=( 2log3 + 2log2+ 6log2 )/(4log2 + log (27/9))

= (2log3 + 8log2)/(4log2 + log 3)

Take 2 common in numerator

= 2(log 3 + 4log2) /(4log2 + log 3)

re arrange terms in numerator

= 2(4log2 + log 3)/(4log2 + log 3)

cancel 4log2 + log 3 common terms

= 2

2 log6 +6log2)/(4log2+log27-log9) = 2

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