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Prove that ((log)a N)/((log)(a b)N)=1+(l...

Prove that `((log)_a N)/((log)_(a b)N)=1+(log)_a b`

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ALLEN-LOGARITHMS-All Questions
  1. Comprehension 3 If P is the non negative characteristic of (log)(10...

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  2. If (log)(10)33. 8=1. 5289 ,\ t h e n(log)(10)0. 338 is- a. 1 .5289 b...

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  3. Prove that ((log)a N)/((log)(a b)N)=1+(log)a b

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  4. log(1//3)sqrt(729*root(3)(9^(- 1)*27^(-4//3))) is equal to

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  5. Compute the following a^(((log)b((log)a N))/((log)b\ \ a))

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  6. Prove the identity; (log)a Ndot(log)b N+(log)b Ndot(log)c N+(log)c Ndo...

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  7. Which is smaller? 2 or (log(("e"-1))2+log2(e-1))

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  8. Solve for x :(l g)4(log)3(log)2x=0

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  9. Find the value of 49^A+5^B w h e r e\ A=1-(log)7 2\ &\ B=-(log)5 4.

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  10. If 4^A+9^B=10^C ,\ where A=(log)(16)4,\ B=(log)3 9\ &\ C=(log)x 83 th...

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  11. Solve the system of equations: (log)a x(log)a(x y z)=48(log)a y loga(x...

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  12. The vlaue of (81^((1)/(log(5)9))+3^((3)/(log(sqrt(6))3)))/(409)((sqrt(...

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  13. Compute the following 56+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)(1//2)...

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  14. The value of 4^(5log(4sqrt(2)(3-sqrt(6))-6log(8)(sqrt(3)-sqrt(2)))) is

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  15. (1/2)^logx^2+2> 3.2^(-"log"(-x))

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  16. Solve (log)x2(log)(2x)2=(log)(4x)2.

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  17. Solve for x :(log)("x"+1)(x^2+x-6)^2=4

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  18. The number of positive integers satisfying x+(log)(10)(2^x+1)=x(log)(1...

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  19. If a^(2) + b^(2) -c^(2) = 0, " then" (1)/("log"(c+a)b) + (1)/("log"(c-...

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  20. Given (log)(10)34. 56=1. 5386 ,\ find (log)(10)3. 456 ;(log)(10)0. 34...

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