log 2 + 16 log 16/15 + 12 log 25/24 + 7 log 81/80
Pl answer clearly with all steps.....
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Answer:
Step-by-step explanation:
Change everything to log 2, log 3, and log 5.
log 2 = log 2
16 log (16/15)
= 16 (log 16 - log 15)
= 16 (log (2^4) - log (3 x 5))
= 16 ((4 log 2 - (log 3 + log 5))
= 64 log 2 - 16 log 3 - 16 log 5
12 log (25/24)
= 12 (log 25 - log 24)= 12 (log 25 - log 24)
= 12 (log (5^2) - log ((2^3) (3)))
= 12 (2 log 5 - (log (2^3) + log 3))
= 12 (2 log 5 - (3 log 2 + log 3))
= - 36 log 2 - 12 log 3 + 24 log 5
7 log (81/80)
= 7 (log 81 - log 80)
= 7 ( log 3^4 - log ((2^4) (5))
= 7 (4 log 3 - (log 2^4 + log 5))
= 7 (3 log 3 - 4 log 2 - log 5)
= - 28 log 2 + 28 log 3 - 7 log 5
Add them = log 2 + log 5 = log 10 = 1
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