Question

(vii)
2 log 6 +6 log 2
4 log 2 + log 27 - log 9
= 2​

Answer 1

2 log 6+ 6log 2

= log 6^2 +log 2^6

= log 36+log64

= log(36x64)

=log2304

now, 4 log2 +log27-log9

=log16+log27-log9

=log48

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

= log 2304 /log48

= log48^2/ log 48

= 2 ( proved)

Answer 2

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

To Find : Verify

Solution:

LHS =

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)

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

= 2

= RHS

QED

Verified

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

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