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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. Solve for x: a) (log(10)(x-3))/(log(10)(x^(2)-21)) = 1/2 b) log(lo...

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  2. If x,y>0 logy x+logx y=10/3 and xy=144 then (x+y)/2=sqrtN where N is a...

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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 product of the positive roots of the equation sqrt((2008))...

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

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  7. Solve the inequality: log(x)2.log(2x)2. log(2)4x gt 1

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  8. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

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

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  10. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=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. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

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  13. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

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  14. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

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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)/7).cos(pi/7)-1=2cos((2pi)/7).

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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. Calculate without using trigonometric tables: (a) 4 cos 20^@ - sqrt3 c...

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  20. (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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