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Question
Find the value of:
`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`
Solution
`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`
= `("log"(125)^(1/2) - "log"(27)^(1/2) - "log"(8)^(1/2))/("log"6 - "log"5)`
= `("log"(5)^(3xx1/2) - "log"(3)^(3xx1/2) - "log"(2)^(3xx1/2))/("log"6 - "log"5)`
= `(3/2 "log"(5) - 3/2"log"(3) - 3/2"log"(2))/("log"(2 xx 3) - "log"5)`
= `(3/2["log"(5) - "log"(3) - "log"(2)])/("log"2 + "log"3 - "log"5)`
= `(3/2["log"(5) - "log"(3) - "log"(2)])/(-["log"5 - "log"3 - "log"2])`
= `-(3)/(2)`.
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