Advertisements
Advertisements
Question
If log√27x = 2 `(2)/(3)` , find x.
Advertisements
Solution
log√27x = 2 `(2)/ (3)`
∴ log√27x = `(8)/ (3)`
∴ x = `( sqrt27 )^((8)/ (3))` ...[ ∵ loga x = b ⇒ x = ab ]
∴ x = `( 27^((1)/(2)))^(8/3)`
∴ x = `( 3 ^((3)/(2)))^(8/3)`
∴ x = `3^((3/2)xx(8/3))`
∴ x = 34
∴ x = 81
APPEARS IN
RELATED QUESTIONS
Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.
Given log10x = 2a and log10y = `b/2`. Write 102b + 1 in terms of 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 ( x + 1) + log ( x - 1) = log 11 + 2 log 3
If 2 log x + 1 = log 360, find: log(2 x -2)
If 2 log x + 1 = log 360, find: log (3 x2 - 8)
If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.
Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers x, y, z?
Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + logp q
Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1
