Question 1091815: prove that,7log(10/9)+3log(81/80)=2log(25/24)+log2
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! One can show they are equivalent
log (10/9)^7*(81/80)^3=log 10^7*9^6, substituting 9^2 for 81
divided by 9^7*(8*10)^3
That reduces to log 10^7/9*512*10^3, where *8^3=512
This is 10^4/512*9=10,000/512*9, or 625/32*9 or log (625/288)
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The right side is log (25^2/24^2)*2
This is log (625/576)*2,, or log (625/288)
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