Advertisements
Advertisements
Question
If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.
Advertisements
Solution
log x = p + q and log y = p - q
`"log"(10x)/y^2` = log 10x - log y2
⇒ `"log"(10x)/y^2` = log10 + logx - 2logy
⇒ `"log"(10x)/y^2` = 1 + p + q - 2(p - q)
⇒ `"log"(10x)/y^2` = 1 - p + 3q.
APPEARS IN
RELATED QUESTIONS
Prove that:
log10 125 = 3(1 - log102).
Simplify : log (a)3 ÷ log a
Express the following in terms of log 5 and/or log 2: log160
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:
`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`
Simplify the following:
`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`
Simplify: log a2 + log a-1
Find the value of:
`("log"sqrt(8))/(8)`
Find the value of:
`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`
