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Prove that 2^{{sqrt(loga 4sqrtab + logb...

Prove that `2^{{sqrt(log_a 4sqrtab + log_b 4sqrtab)-sqrt((log_a)4sqrt(b/a)+log_b 4sqrt(a/b))}sqrt(log_a b))= { 2 , b gea gt1`and `2^(log_b a) , 1 ltblta`

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Prove that 2^{{sqrt(log_a 4sqrtab + log_b 4sqrtab)-sqrt((log_a)4sqrt(b/a)+log_b 4sqrt(a/b))}sqrt(log_a b))= { 2 , b gea gt1and 2^(log_b a) , 1 ltblta

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BANSAL-LOGARITHM-All Questions
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  3. Find the number of integral solution of the equation log(sqrt(x))(x+|x...

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  4. Suppose p , q ,r and s in NN satisfying the relation p+1/(q+1/(r+1/s))...

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  5. If x and y are real numbers, such that 2log(2y-3x)=logx+logy, then fin...

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  8. If log(3)M=a1+b1 and log5M=a2+b2 where a1,a2 in N and b1,b2 in [0,1). ...

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  9. If log(3x) 45 = log(4x) 40sqrt3 then find the characteristic of x^3...

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  10. If (x1, y1)&(x2, y2) are the solutions of the equaltions, (log)(225)(x...

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  11. Prove that 2^{{sqrt(loga 4sqrtab + logb 4sqrtab)-sqrt((loga)4sqrt(b/a...

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  12. Find the value of x satisfying the equation, sqrt((log3(3x)^(1/3)+logx...

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  13. Given that log2 a=s, log4 b=5^2 and log(c^2) (8)=2/(s^3+1). Write log2...

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  14. let y=sqrt(log23log2(12)log2(48)log2(192)+16)-log2(12)log2(48)+10find ...

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  15. The least value of the expression 2(log)(10)x-(log)x(0. 01), for x &g...

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  16. Solve: (log)((2x+3))(6x^2+23x+21)+(log)((3x+7))(4x^2+12 x+9)=4

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  17. The equation x^((3/4)(log2 x)^2 + (log2 x) - (5/4))=sqrt(2) has (1)a...

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  18. The number of solutions of (log)4(x-1)=(log)2(x-3) is (2001, 2M) 3 (b...

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  19. Let (x0,y0) be the solution of the following equations: (2x)^ln2 = (3y...

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  20. The value of 6+(log)(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqr...

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