Advertisements
Advertisements
प्रश्न
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
उत्तर
`[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
= `[ 3 xx (3^2)^(n + 1) - 3^2 xx 3^(2n)]/[ 3 xx 3^(2n + 3) - (3^2)^(n + 1)]`
= `[ 3^( 1 + 2n + 2) - 3^( 2 + 2n )]/[3^(1 + 2n + 3) - 3^( 2n + 2 )]`
= `[ 3^( 3 + 2n ) - 3^( 2 + 2n )]/[3^(4 + 2n) - 3^( 2n + 2 )]`
= `[ 3^(2n)( 3^3 - 3^2 )]/[3^(2n)(3^4 - 3^2)]`
= `[ 27 - 9 ]/[ 81 - 9 ]`
= `18/72`
= `1/4`
APPEARS IN
संबंधित प्रश्न
Solve for x:
`3^(4x + 1) = (27)^(x + 1)`
Find x, if : 42x = `1/32`
Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`
If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`
Evaluate the following:
`(4^3 xx 3^7 xx 5^6)/(5^8 xx 2^7 xx 3^3)`
Evaluate the following:
`(1 - 15/64)^(-1/2)`
Find the value of k in each of the following:
`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3k
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)3 = 27xyz
Prove the following:
`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1
