Advertisements
Advertisements
प्रश्न
If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
Show that : m - n = 1.
Advertisements
उत्तर
`[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
⇒ `[ 3^(2n). 3^2 . 3^n - (3)^(3n)]/[3^(3m) . (2)^3] = 1/3^3`
⇒ `[ 3^(3n) . 3^2 - 3^(3n) ]/[ 3^(3m) . 2^3 ] = 1/3^3`
⇒ `[ 3^(3n)( 3^2 - 1 ) ]/[ 3^(3m) xx 8 ] = 1/3^3`
⇒ `[ 3^(3n) xx 8 ]/[ 3^(3m) xx 8 ] = 1/3^3`
⇒ `1/[ 3^(3( m - n ))] = 1/3^( 3 xx 1 )`
⇒ m - n = 1 ( proved )
APPEARS IN
संबंधित प्रश्न
Solve for x : (13)√x = 44 - 34 - 6
If 34x = ( 81 )-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `
Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`
Write each of the following in the simplest form:
a2 x a3 ÷ a4
Simplify the following:
`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`
Simplify the following:
`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`
Simplify the following:
`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`
Simplify the following:
`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`
