Advertisements
Advertisements
Question
Find x, if : `(root(3)( 2/3))^( x - 1 ) = 27/8`
Advertisements
Solution
`(root(3)( 2/3))^( x - 1 ) = 27/8`
`[(2/3)^(1/3)]^( x - 1 ) = 3^3/2^3`
⇒ `(2/3)^[( x - 1 )/3] = (3/2)^3`
⇒ `(2/3)^[( x - 1 )/3] = (2/3)^-3`
We know that if bases are equal, the powers are equal
⇒ `[ x - 1 ]/3 = -3`
⇒ x - 1 = - 9
⇒ x = - 9 + 1
⇒ x = - 8
APPEARS IN
RELATED QUESTIONS
Solve for x:
`3^(4x + 1) = (27)^(x + 1)`
Solve for x:
`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
If 5-P = 4-q = 20r, show that : `1/p + 1/q + 1/r = 0`
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`
Evaluate the following:
`(4^3 xx 3^7 xx 5^6)/(5^8 xx 2^7 xx 3^3)`
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Find the value of k in each of the following:
`root(4)root(3)(x^2)` = xk
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
Prove the following:
`("a"^"m"/"a"^"n")^("m"+"n"+1) ·("a"^"n"/"a"^1)^("n" + 1-"m").("a"^1/"a"^"m")^(1+"m"-"n")`
