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Question
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
Solution
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
= `("log"(27)^(1/2) + "log"2^3 + "log"1000^(1/2))/("log"(3 xx 2^2 xx 10)`
= `("log"(3)^(3xx1/2) + "log"2^3 + "log"(10)^(3xx1/2))/("log"3 + "log2^2 + "log 10)`
= `(3/2"log"3 + 3"log"2 + 3/2"log"(10))/("log"3 + 2 "log"2 + "log"10)`
= `(3/2"log"3 + 3/2(2"log"2) + 3/2(1))/("log"3 + 2"log2 + 1)`
= `(3/2["log" 3 + 2"log" 2 + 1])/("log"3 + 2"log2 + 1)`
= `(3)/(2)`.
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