7Log 16/15+5Log 25/24 +3Log 81/80=log 2
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Step by step solution:
The given expression E is,
E = 7 log (16/15) + 5 log (25/24) + 3 log (81/80)
= log (16/15)⁷ + log (25/24)⁵ + log (81/80)³
= log [ (16/15)⁷ × (25/24)⁵ × (81/80)³] —(1)
Now
(16/15)⁷ = (2⁴/3¹.5¹)⁷ = (2²⁸/3⁷.5⁷)
(25/24)⁵ = (5²/2³.3¹)⁵ = (5¹⁰/2¹⁵. 3³)
(81/80)³ = (3⁴/2⁴. 5¹)³ = (3¹²/2¹².5³)
So
[ (16/15)⁷ × (25/24)⁵ × (81/80)³]
= [{2²⁸ . 3¹² . 5¹⁰}/{2²⁷ . 3¹² . 5¹⁰}] = 2
Therefore,
E = log 2.
Hope it will clear your doubt
Thank you for asking
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