Advertisements
Advertisements
Question
If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
Show that : m - n = 1.
Solution
`[ 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
RELATED QUESTIONS
Simplify : a2 − 2a + {5a2 − (3a - 4a2)}
Simplify : `"x" − "y" − {"x" − "y" − ("x" + "y") −overline("x"-"y")}`
Simplify : −3 (1 − x2) − 2{x2 − (3 − 2x2)}
Simplify: (x5 ÷ x2) × y2 × y3
Write each of the following in the simplest form:
(a3)5 x a4
Write each of the following in the simplest form:
`"a"^(1/3) ÷ "a"^(-2/3)`
Write each of the following in the simplest form:
a-3 x a2 x a0
Write the following in the simplest form:
(b-2 - a-2) ÷ (b-1 - a-1)
Simplify the following:
`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`
Simplify the following:
`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`
