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Show that 7log(10/9) – 2log(25/24) 3log(80/81) = log 2

1 Answer

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Answer:

7log(10/9) = 7(log 10 - log 9)

= 7(log 5 + log 2 - 2 log 3)

2log(25/24) = 2(log 25 - log 24)

= 2(2 log 5 - (log 8 + log 3))

= 2(2 log 5 - 3 log 2 - log 3)

3log(80/81) = 3(log 80 - log 81)

= 3(log 16 + log 5 - 4 log 3)

= 3(4 log 2 + log 5 - 4 log 3)

7log(10/9) - 2log(25/24) - 3log(80/81) =

7 log 5 + 7 log 2 - 14 log 3 - 4 log 5 +

6 log 2 + 2 log 3 - 12 log 2 - 3 log 5 +

12 log 3 = log 2

User Moudy
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