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Prove root(ln)((x^(l))/(x^(n)))xxroot(...

Prove
`root(ln)((x^(l))/(x^(n)))xxroot(nm)((x^(n))/(x^(m)))xxroot(ml)((x^(m))/(x^(l)))=1`

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Find the value of root(ln)((x^l)/(x^n))xxroot(mn)((x^n)/(x^m))xxroot(lm)((x^m)/(x^l)) .

If a+b+c =0 Prove that root(bc)(x^(a^(2))/x^(bc))xxroot(ca)(x^(b^(2))/x^(ca))xxroot(ab)(x^(c^(2))/x^(ab))=1

Prove root(p+q)(x^(p^(2))/(x^(q^(2))))xxroot(q+r)(x^(q^(2))/(x^(r^(2))))xxroot(r+p)(x^(r^(2))/(x^(p^(2))))=1

Prove that : ((x^m)/(x^n))^(m+n) xx((x^n)/(x^l))^(n+l)xx((x^l)/(x^m))^(l+m) =1 .

Prove that : ((x^m)/(x^n))^(m+n-l) xx((x^n)/(x^l))^(n+l-m)xx((x^l)/(x^m))^(l+m-n) =1 .

Simply (x^(m)/x^(n))^(m^(2)+mn+n^(2))xx(x^(n)/x^(l))^(n^(2)+nl+l^(2))xx(x^(l)/x^(m))^(l^(2)+lm+m^(2))

Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p-m)+x^(p-n)) .

If x^(m)*y^(n)=(x+y)^(m+n) , show that (dy)/(dx)=(y)/(x) .

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+ to n terms =(n)/(1-x)-(x(1-x^(n)))/(1-x)^(2)

CHHAYA PUBLICATION-LAWS OF INDICES-Short Answer Type Questions
  1. Prove (1/(1+x^(b-a)+x^(c-a)))+(1/(1+x^(a-b)+x^(c-b)))+(1/(1+x^(a-c)+...

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  2. Prove root(p+q)(x^(p^(2))/(x^(q^(2))))xxroot(q+r)(x^(q^(2))/(x^(r^(2...

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  3. Prove root(ln)((x^(l))/(x^(n)))xxroot(nm)((x^(n))/(x^(m)))xxroot(ml)...

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  4. If x=2^(2/3)+2^(1/3) show that x^(3)-6x=6

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  5. If a=2^(1/3)-2^(-1/3) show that 2a^(3)+6a-3=0

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  6. If x=2+2^(2/3)+2^(1/3) show that x^(3)-6x^(2)+6x-2=0

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  7. If x^(1/a)=y^(1/b)=z^(1/c ) and xyz =1 show that a+b+c=0

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  8. If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc

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  9. If x^(a)=y^(b)=(xy)^(c ) prove that ab=c(a+b)

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  10. If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc

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  11. If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y t...

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  12. If p^(a)=q^(b)=r^(c ) and pqr=1 show that ab+bc+ca=0

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  13. If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)

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  14. If (a-(1)/(a))^(2)=3 show that a^(6)+(1)/(a^(6))=110

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  15. If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)

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  16. If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive num...

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  17. If (x^(n^3))^(n)=(x^(3^n))^(3) show that root(n+1)(n^(4))=3

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  18. If x^(p^q)=(x^sqrt(p))^(q) find p in terms of q

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  19. If (56)^(a)=(5.6)^(b)=10^(c ) show that (1)/(a)=(1)/(b)+(1)/(c )

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  20. 6^(2x+4)=3^(3x).2^(x+8)

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