Advertisements
Advertisements
Question
If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.
Advertisements
Solution
x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108
⇒ x = log 108 - log 4 - 2 log 5 - 3 log 3 - 2 log 2
= log (22 . 33) - log 22 - log 52 - log 33 - log 22
= `"log"((2^2. 3^3)/(2^2 . 5^2 . 3^3. 2^2))`
= `"log"(1/100)`
⇒ x
= log 1 - log 100
= 0 - 2
= -2
∴ x = -2.
APPEARS IN
RELATED QUESTIONS
If a2 + b2 = 23ab, show that:
log `(a + b)/5 = 1/2`(log a + log b).
If log√27x = 2 `(2)/(3)` , find x.
Solve for x and y ; if x > 0 and y > 0 ; log xy = log `x/y` + 2 log 2 = 2.
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.
Solve for x, if : logx49 - logx7 + logx `1/343` + 2 = 0
Express log103 + 1 in terms of log10x.
State, true of false:
logba =-logab
State, true of false:
If `("log"49)/("log"7)` = log y, then y = 100.
If 2 log x + 1 = log 360, find: log (3 x2 - 8)
