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If a^x=b^y=c^z" and "abc=1, then prove t...

If `a^x=b^y=c^z" and "abc=1`, then prove that `xy+yz+zx=0`.

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`xy+yz+zx=0`
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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. If a^x=b^y=c^z" and "abc=1, then prove that xy+yz+zx=0.

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  2. (x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

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  3. (x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

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  4. [{(2^(-1))^(-1)}^(-1)]^(-1)=

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  5. The value of {(x^(-5))^(2/3)}^(-3/10) is

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  6. Which one of the following numbers is the greatest ? 2^(30),3^(24),4^(...

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  7. Which one of the following numbers is the smallest? 3^(1/3),2^(1/2),4^...

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  8. [{(a^(-1))^(-1)}^(-1)]^(-1)=

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  9. If 49^x = 7^3, then x=

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  10. If 4 xx8^x = 256, then (-x)^(-x)=

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  11. root(5)(x^8sqrt(x^8sqrt(x^(-8))))=

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  12. Find the value of (((8a^3)/(27x^(-3)))^(2/3)xx((64a^3)/(27x^(-3)))^(-2...

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  13. Simplify root(3)(a^(-2)).b xx root(3)(b^(-2)).c root(3)(c^(-2)).a.

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  14. If a^x=b,b^y =c,c^z=a, find the value of xyz.

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  15. Calculate : 9^(-3)xx((16)^(1/4))/(6^(-2))xx((1)/(27))^(-4/3).

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  16. If x^y=y^x, then prove that (x/y)^(x/y)=(x)^((x)/(y)-1).

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  17. Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b).

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  18. Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(...

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  19. Factorise : (a+b).

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  20. Find the value of ((bc)^(b-c)(ca)^(c-a)(ab)^(a-b))/((a^(b-c)b^(c-a)c^(...

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  21. If p=a^x,q=a^y" and "a^2=(p^yq^x)^z, then find the value of xyz.

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