Advertisements
Advertisements
Question
Solve the following:
`log_2x + log_4x + log_16x = (21)/(4)`
Advertisements
Solution
`log_2x + log_4x + log_16x = (21)/(4)`
∴ `(1)/("log"_x2) + (1)/("log"_x2^2) + (1)/("log"_x2^4) = (21)/(4)`
∴ `(1)/("log"_x2) + (1)/("2log"_x2) + (1)/("4log"_x2) = (21)/(4)`
∴ `(1)/("log"_x2) (1 + 1/2 + 1/4) = (21)/(4)`
∴ `(1)/("log"_x2)(7/4) = (21)/(4)`
∴ `"log"_x2 = (7)/(4) . (4)/(21)`
∴ `"log"_x2 = (1)/(3)`
∴ `x^(1/3)` = 2
∴ x = 23
= 8.
APPEARS IN
RELATED QUESTIONS
Find x, if : logx 625 = - 4
If log2(x + y) = log3(x - y) = `log 25/log 0.2`, find the values of x and y.
Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.
Solve for x, if : logx49 - logx7 + logx `1/343` + 2 = 0
If a2 = log x , b3 = log y and `a^2/2 - b^3/3` = log c , find c in terms of x and y.
Given x = log1012 , y = log4 2 x log109 and z = log100.4 , find :
(i) x - y - z
(ii) 13x - y - z
Solve the following:
log 7 + log (3x - 2) = log (x + 3) + 1
State, true of false:
If `("log"49)/("log"7)` = log y, then y = 100.
If log x = a and log y = b, write down
10a-1 in terms of x
If log 3 m = x and log 3 n = y, write down
`3^(1-2y+3x)` in terms of m an n
