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Solve the system of equations: (log)a x(...

Solve the system of equations: `(log)_a x(log)_a(x y z)=48(log)_a y log_a(x y z)=12 ,\ a >0,\ a!=1(log)_a z log_a(x y z)=84\ `

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`(a^(4),a,a^(7))` or `(1/a^(4), 1/a, 1/a^(7))`
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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. If a, b, c are positive numbers such that a^(log(3)7) =27, b^(log(7)1...

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  2. Solve for x: a) log(x)2. log(2x)2 = log(4x)2 b) 5^(logx)+5x^(log5...

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

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  4. Solve the equation for x:x^(logx+4) = 32, where base of logarithim is ...

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  5. Find the production of the positive roots of the equation sqrt2000(x)^...

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  6. Solve the inequality: log(1//2)(x+1) gt log(2)(2-x)

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  7. The set of real values of x for which (log(x)2)(log(x)2)(log(2)4x) ...

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  8. about to only mathematics

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  9. Prove that cos 2a=2sin^(2)beta+4cos (alpha+beta)sin alpha sin beta+cos...

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  10. Prove that: s in^4pi/8+s in^4(3pi)/8+s in^4(5pi)/8+s in^4(7pi)/8=3/2

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  11. If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot...

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  12. If tan.(pi)/(24)=(sqrt(p)-sqrt(q))(sqrt(r )-s), then the value of p+q+...

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  13. If m tan (theta - 30^(@))= n tan (theta + 120^(@)), show that cos 2 th...

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  14. It cos(alpha+beta)=4/5,sin(alpha-beta)=5/(13)a n dalpha,beta lie betwe...

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  15. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  16. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  17. Prove that 4cos(2pi)/7dotcospi/7-1=2cos(2pi)/7dot

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  18. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  19. Evaluate (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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  20. Solve cos^6(pi/16)+cos^6((3pi)/16)+cos^6((5pi)/16)+cos^6((7pi)/16)

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