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
Solve for x and y ; if x > 0 and y > 0 ; log xy = log `x/y` + 2 log 2 = 2.
Find x, if : logx 625 = - 4
Show that : loga m ÷ logab m + 1 + log ab
Given log10x = 2a and log10y = `b/2`. Write 102b + 1 in terms of y.
Given log10x = 2a and log10y = `b/2. "If" log_10^p = 3a - 2b`, express P in terms of x and y.
Solve for x, `log_x^(15√5) = 2 - log_x^(3√5)`.
Evaluate: `(log_5 8)/(log_25 16 xx Log_100 10)`
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
