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Simplify: 1/(1+(log)a b c)+1/(1+(log)b c...

Simplify: `1/(1+(log)_a b c)+1/(1+(log)_b c a)+1/(1+(log)_c a b)`

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If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

Prove that : (1)/( log _(a) ^(abc) )+(1)/(log_(b)^(abc) ) + (1)/( log _c^(abc)) =1

1/(1+log_b a+log_b c)+1/(1+log_c a+log_c b)+1/(1+log_a b+log_a c)

Evaluate : (1)/(log_(a)bc + 1) + (1)/(log_(b)ca + 1) + (1)/(log_(c) ab + 1)

The sum of the series: 1/((log)_2 4)+1/((log)_4 4)+1/((log)_8 4)++1/((log)_(2n)4) is (n(n+1))/2 (b) (n(n+1)(2n+1))/(12) (c) (n(n+1))/4 (d) none of these

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If (log)_a x=p\ a n d(log)_b x^2=q ,\ t h e n(log)_xsqrt(a b) is equal to (where a ,\ b ,\ x in R^+-{1} )- a. 1/p+1/q b. 1/(2p)+1/q c. 1/p+1/(2q) d. 1/(2p)+1/(2q)

CENGAGE ENGLISH-LOGARITHM-All Questions
  1. Find the value of (1/(49))^(1+(log)7 2)+5^(-1(log)((1/5))(7))

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  2. Prove that: 2^((sqrt((log)a4sqrt(a b)+(log)b4sqrt(a b))-sqrt((log)a4sq...

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  3. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

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  4. Solve (log)4 8+(log)4(x+3)-(log)4(x-1)=2.

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  5. Which of the following pairs of expression are defined for the same se...

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  6. Solve (log)2(3x-2)=(log)(1/2)x

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  7. Solve log(-x)=2log(x+1)dot

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  8. Solve: (log)2(4.3^x-6)-(log)2(9^x-6)=1.

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  9. Solve 2^(x+2)27^(x//(x-1))=9

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  10. Suppose x , y ,z=0 and are not equal to 1 and logx+logy+logz=0. Find t...

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  11. If (log)(12)27=a , then find (log)6 16int e r m sofa

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  12. If y^2=x z and a^x=b^y=c^z , then prove that (log)ab=(log)bc

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  13. Simplify: 1/(1+(log)a b c)+1/(1+(log)b c a)+1/(1+(log)c a b)

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

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  15. Find the value of ((log)3 4)((log)4 5)((log)5 6)((log)6 7)((log)7 8)((...

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  16. y=2^(1/((log)x4), then find x in terms of y.

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  17. If n >1,t h e np rov et h a t 1/((log)2n)+1/((log)3n)++1/((log)(53)n)...

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  18. What is logarithm of 32 root(5) 4" to the base "2sqrt2?

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  19. Which is greater: x=(log)3 5ory=(log)(17)25 ?

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  20. The product of roots of the equation (3)/((log8x)^2)=3 is 1 (b) (c)...

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