Advertisements
Advertisements
Question
Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers x, y, z?
Advertisements
Solution
log (1 + 2 + 3) = log 6
= log (1 + 2 + 3) = log 1 + log 2 + log 3
No, this property is not true for any numbers x, y, z
For example, log (1 + 3 + 5) = log 9
log 1 + log 3 + log 5 = log (1 x 3 x 5) = log 15
log (1 + 3 + 5) ≠ log 1 + log 3 + log 5.
APPEARS IN
RELATED QUESTIONS
Find x, if : logx 625 = - 4
Show that : loga m ÷ logab m + 1 + log ab
If p = log 20 and q = log 25 , find the value of x , if 2log( x + 1 ) = 2p - q.
Given x = log1012 , y = log4 2 x log109 and z = log100.4 , find :
(i) x - y - z
(ii) 13x - y - z
Solve for x: `("log"27)/("log"243)` = x
Solve for x: `("log"81)/("log"9)` = x
If log 3 m = x and log 3 n = y, write down
`3^(1-2y+3x)` in terms of m an n
If 2 log x + 1 = log 360, find: x
If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5a+b-c = 1
Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + logp q
