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if a,b,c are positive real numbers such that `a^(log_3(7));b^(log_7(11))=49 and c^(log_11(25))=sqrt(11)` find the vale of `a^((log_3(7))^2)+b^((log_7(11))^2)+c^((log_11(25))^2)`

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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Find the square of the sum of the roots of the equation log(3)x.log(...

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  2. Find the value of 49^(1-log(7)2)+5^(-log(5)4)

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  3. if a,b,c are positive real numbers such that a^(log3(7));b^(log7(11))=...

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

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

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

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

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

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

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

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  13. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

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

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  15. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

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

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

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

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

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  20. Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7).

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