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Solve for x :5^(logx)+5x^(log5)=3(a >0);...

Solve for `x :5^(logx)+5x^(log5)=3(a >0);` where base of `log` is a

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ALLEN -LOGARITHMS-All Questions
  1. Compute the following 56+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)(1//2)...

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

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

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

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

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

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

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  9. Find the number of positive integers which have the characteristics 3 ...

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  10. If (log)(10)2=0. 3010\ &(log)(10)3=0. 4771.\ Find the value of (log...

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  11. If log(10)2=0.3010 ,\ log(10)3=0.4771. Find the number of integers in ...

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  12. Find the antilogarithm of 0.75 if the base of the logarithm is 2401.

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  13. If x ,y >0,(log)y x+(log)x y=(10)/3 and x y=144 , then (x+y)/2=sqrt(...

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  14. let y=sqrt(log2(3)log2(12)log2(48)log2(192)+16)-log2(12)log2(48)+10fin...

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  15. If x=1+(log)a b c , y=1+(log)b c a and z=1+(log)c a b , then prove ...

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  16. A rational number which is 50 times its own logarithm to the base 10, ...

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  17. Prove that a^x-b^y=0 where x=sqrt((log)a b), y=sqrt((log)b a), a >0, b...

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  18. If ((log)a N)/((log)c N)=((log)a N-(log)b N)/((log)b N-(log)c N), wher...

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  19. If (log)b a(log)c a+(log)a b(log)c b+(log)a c(log)bc=3 (where a , b , ...

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  20. Prove that (log)7 10 is greater than (log)(11)13.

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