Advertisements
Advertisements
Question
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
Advertisements
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)`.
APPEARS IN
RELATED QUESTIONS
If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2
If log5 x = y, find 52y+ 3 in terms of x.
Express the following in terms of log 2 and log 3: log 36
Write the logarithmic equation for:
n = `sqrt(("M"."g")/("m".l)`
Write the logarithmic equation for:
V = `(1)/("D"l) sqrt("T"/(pi"r")`
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
Express the following as a single logarithm:
`2 + 1/2 "log" 9 - 2 "log" 5`
Express the following as a single logarithm:
`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`
If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540
If log 27 = 1.431, find the value of the following: log 9
