Advertisements
Advertisements
प्रश्न
If x2 + y2 = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)
Advertisements
उत्तर
x2 + y2 = 7xy
⇒ x2 + y2 - 2xy = 7xy - 2xy
⇒ (x + y)2 = 9xy
⇒ `((x + y)/3)^2` = xy
⇒ `((x + y)/3) = sqrt(xy)`
Considering log both sides, we get
`"log"((x + y)/3) = "log"(xy)^(1/2)`
⇒ `"log"((x + y)/3) = (1)/(2)"log"(xy)`
⇒ `"log"((x + y)/3) = (1)/(2)["log" x + "log" y]`.
APPEARS IN
संबंधित प्रश्न
Given 3log x + `1/2`log y = 2, express y in term of x.
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25
Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.
Given log x = 2m - n , log y = n - 2m and log z = 3m - 2n , find in terms of m and n, the value of log `(x^2y^3 ) /(z^4) `.
Express the following in terms of log 2 and log 3: `"log"root(5)(216)`
Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`
Express the following as a single logarithm:
`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`
Simplify the following:
`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`
If 2 log x + 1 = 40, find: log 5x
If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45
