Advertisements
Advertisements
प्रश्न
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
उत्तर
`("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
संबंधित प्रश्न
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25
Given: log3 m = x and log3 n = y.
Express 32x - 3 in terms of m.
Simplify : log (a)3 ÷ log a
Express the following in terms of log 2 and log 3: log 36
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
Express the following as a single logarithm:
`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`
If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.
If 2 log x + 1 = 40, find: log 5x
If 2 log y - log x - 3 = 0, express x in terms of y.
If x2 + y2 = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)
