prove that:- 7log16/15+5log25/24+3log81/80= log2

Dear Student,

7log(16/15) + 5log(25/24) + 3log(81/80)

= log[(16/15)^7] + log[(25/24)^5] + log[(81/80)^3]

= log{[(16^7)*(25^5)*(81^3)] / [(15^7)*(24^5)*(80^3)]}

= log{[(2^28)*(5^10)*(3^12)] / [(3^7)*(5^7)*(2^15)*(3^5)*(2^12)*(5^3]}

= log{[(2^28)*(3^12)*(5^10)] / [(2^27)*(3^12)*(5^10)}

= log(2)

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