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If f(n)=prod(i=2)^(n-1)logi(i+1), the va...

If `f(n)=prod_(i=2)^(n-1)log_i(i+1)`, the value of `sum_(k=1)^100f(2^k)` equals

A

5010

B

5050

C

5100

D

5049

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The correct Answer is:
B
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ARIHANT MATHS-LOGARITHM AND THEIR PROPERTIES-Exercise (Single Option Correct Type Questions)
  1. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

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  2. There exists a positive number k such that log2x+ log4x+ log8x= logkx...

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  3. If x1,x2 & x3 are the three real solutions of the equation x^(log10^2...

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  4. If f(n)=prod(i=2)^(n-1)logi(i+1), the value of sum(k=1)^100f(2^k) equa...

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  5. If x-1/x=m then the value of x^3-1/x^3 is :

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  6. In Which quadrant Point (-2,3) will be lie.

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  7. Solve for x if x(x-4)= -4

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  8. If xn > x(n-1) > ..........> x3 > x1 > 1. then the value of log(x1) [...

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  9. If (x(y+z-x))/log x = (y(z+x-y))/log y = (z(x+y-z))/log z ," prove th...

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  10. If y = a^(1/(1-log(a) x)) and z = a^(1/(1-log(a)y))",then prove that ...

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  11. If (log)(0. 3)(x-1)<(log)(0. 09)(x-1), then x lies in the interval (...

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  12. The value of a^x-b^y is (wherex=sqrt(logab)and y=sqrt(logba),agt0,bgt0...

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  13. If x=1+log(a) bc, y=1+log(b) ca, z=1+log(c) ab, then (xyz)/(xy+yz+zx) ...

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  14. The value of a^((logb(logbN))/(logb a)), is

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  15. Find the value of 49^((1-log7(2)))+5^(-log5(4) is

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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. Solve the equation x^(log(x)(x+3)^(2))=16.

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  18. The point on the graph y=log2log6{2^sqrt(2x+1)+4} whose y coordinate i...

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  19. Find dy/dx ,if 2x^2-xy+4y^2 = 200

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  20. The values of x, satisfying the equation for AA a > 0, 2log(x) a + lo...

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