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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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Prove the identity; (log)_(a)N log_(b)N+(log)_(b)N log_(c)N+(log)_(c)N log_(a)N=((log)_(a)N log_(b)N log_(c)N)/((log)_(abc)N)

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

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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+(log)2e-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. Value of [2/((log)4(2000)^6)+3/((log)5(2000)^6)] is 4^(1/3). 5^(1//2) ...

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

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  13. Compute the following (81^(1/((log)5 9))+3^(3/((log)(sqrt(6))3)))/(409...

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

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  15. 4^(5 log(4sqrt(2)) (3-sqrt(6)) - 6 log8(sqrt(3)-sqrt(2)))

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  16. Solve for x :5^(logx)+5x^(log5)=3(a >0); where base oflog\ is a

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

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

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  19. Solve for x : x+(log)(10)(1+2^x)=xdot(log)(10)5+log(10)6

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  20. Given a^2+b^2=c^2&\ a .0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ prove that ...

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