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If a = 1 + log(x) yz, b = 1 + log(y) zx...

If ` a = 1 + log_(x) yz, b = 1 + log_(y) zx and c = 1 + log xy ` where x, y, z are positive real numbers
different unity , them prove that abc = ab + bc + ca

A

0

B

2abc

C

abc

D

`a^(2) + b^(2) + c^(2)`

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Exercise
  1. If "log"(2) 7 = x, then x is:

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  2. If 2^((3)/("log"(3)x)) = (1)/(64), then x =

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  3. If a = 1 + log(x) yz, b = 1 + log(y) zx and c = 1 + log xy where x, ...

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  4. If (logx)/(a^2+a b+b^2)=(logy)/(b^2+b c+c^2)=(logz)/(c^2+c a+a^2), the...

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  5. If log(2a-3b)=loga-logb, then a=

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  6. If ("log"3)/(x-y) = ("log"5)/(y-z) = ("log" 7)/(z-x), " then " 3^(x+y)...

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  7. ("log"(2)a)/(3) = ("log"(2)b)/(4) = ("log"(2)c)/(5lambda) " and " a^(-...

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  8. if loga/(b-c)=logb/(c-a)=logc/(a-b) then find the value of a^ab^bc^c

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  9. The value of (0.16)^log2.5{1/3+1/3^2+...} is

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  10. if a^2+4b^2=12ab, then log(a+2b)

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  11. Find the value of 7 log(16/15) + 5 log (25/24) + 3 log (81/80).

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  12. If 1/2logx+1/2logy+log2=log(x+y) then :

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  13. The number of real solutions of the equation "log" (-x) = 2"log" (x+1)...

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  14. The solution of the equation "log"pi("log"(2) ("log"(7)x)) = 0, is

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  15. If "log"(4) 2 + "log"(4) 4 + "log"(4) 16 + "log"(4) x = 6, then x =

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  16. The number of real values of the parameter k for which (log(16)x)^(2) ...

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  17. If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

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  18. The value of "log"(b)a xx "log"(c) b xx "log"(a)c, is

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  19. If "log"(a) ab = x, then the value of "log"(b)ab, is

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  20. If x=-2, then the value of "log"(4)((x^(2))/(4)) -2 "log"(4)(4x^(4)), ...

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