Advertisements
Advertisements
Question
Find the value of:
`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`
Advertisements
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)`.
APPEARS IN
RELATED QUESTIONS
If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 12
If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2
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"root(5)(216)`
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
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 2 log x + 1 = 40, find: x
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
