Question

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

Answer 1

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

= `12 "log" (3)/(2) + 7"log" (5^3)/(3^3) - 5 "log" (5^2)/(2^2 xx 3^2) - 7"log" 5^2 + "log" (2^4)/(3)`

= 12 log 3 − 12 log 2 + 7 log 5³ − 7 log 3³ − 5 log 5² + 5 log 2² + 5 log 3² − 7 log 5² + log 2⁴ − log 3

= 12 log 3 − 12 log 2 + 21 log 5 − 21 log 3 − 10 log 5 + 10 log 2 + 10 log 3 − 14 log 5 + 4 log 2 − log 3

= 2 log 2 + 3 log 5