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 27 = 1.431, find the value of : log 9
Prove that : If a log b + b log a - 1 = 0, then ba. ab = 10
If 2 log y - log x - 3 = 0, express x in terms of y.
Express the following in terms of log 2 and log 3: log 54
Express the following in terms of log 5 and/or log 2: log20
Express the following in terms of log 5 and/or log 2: log160
Write the logarithmic equation for:
E = `(1)/(2)"m v"^2`
Simplify the following:
`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`
If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12
If log 4 = 0.6020, find the value of each of the following: log8
