Advertisements
Advertisements
प्रश्न
Prove the following:
(xa)b-c x (xb)c-a x (xc)a-b = 1
Advertisements
उत्तर
L.H.S.
= (xa)b-c x (xb)c-a x (xc)a-b
= `x^("a"("b"-"c")) xx x^("b"("c"-"a")) xx x^("c"("a"-"b"))` .....(Using (am)n = amn)
= `x^("ab"-"ac") xx x^("bc"-"ab") xx x^("ac"-"bc")`
= `x^("ab"-"ac"+"bc"-"ab"+"ac"-"bc")` .....(Using am x an = am+n)
= x°
=1
= R.H.S
= Hence proved.
APPEARS IN
संबंधित प्रश्न
Solve for x:
`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.
Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
Solve : 3x-1× 52y-3 = 225.
Evaluate the following:
`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`
Solve for x:
`"p"^-5 = (1)/"p"^(x + 1)`
Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`
If 2250 = 2a. 3b. 5c, find a, b and c. Hence, calculate the value of 3a x 2-b x 5-c.
Prove the following:
`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1
