Logs!!..But no wood..- part 3

Algebra Level 2

Find the value of 7 log ⁡ ( 16 15 ) + 5 log ⁡ ( 25 24 ) + 3 log ⁡ ( 81 80 ) 7\log { \left( \frac { 16 }{ 15 } \right) } +5\log { \left( \frac { 25 }{ 24 } \right) } +3\log { \left( \frac { 81 }{ 80 } \right) }

log ⁡ 3 \log { 3 } 0 0 log ⁡ 2 \log { 2 } log ⁡ 4 \log { 4 }

Krishna Ramesh by Krishna Ramesh , 22, India

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1 solution

Sissi Jian
Jul 14, 2015

7log(16/15)+5log(25/24)+3log(81/80) =log(2^4/3 5)^7+log(5^2/2^3 3)^5+log(3^4/5 2^4)^3 =log((2^28/3^7 5^7) (5^10/2^15 3^5) (3^12/5^3 2^12)) then cancel out 2s, 3s, and 5s. =log(2)

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