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If a/b=c/d=e/f and (2a^4b^2+3a^2c^2-5e^4...

If `a/b=c/d=e/f` and `(2a^4b^2+3a^2c^2-5e^4f)/(2b^6+3b^2d^2-5f^5)=(a/b)^n` then find the value of n.

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The correct Answer is:
`a^(4)/ b^(4)`
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If (a)/(b)=(c)/(d)=(e)/(f) and (2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(2b^(6)+3b^(2)d^(2)-5f^(5))=((a)/(b))^(n) then find the value of n.

When two ratios are equal, then the four quantities compositing them are said to be proportiona. If a/b=c/d, then it is written a:b=c:dor a:b::c:d. Also if a/b=c/d=lamdaimpliesa=blamdaand c=dlamdaimpliesa/b=c/d =(a+-c)/(b+-d)=(""^(n)sqrt((a)^(n)+-(c)^(n)))/(""^(n)sqrt((b)^(n)+-(d)^(n)))=lamda(lamdagt0) important property of proportion : 1. If a:b=c:d,then (a+b)/(b)=(c+d)/(d)("Componendo")i.e.(a)/(b)=(c)/(d)implies(a)/(b)+1=(c)/(d)+1 2. If a:b=c"d, then (a-b)/(b)=(c-d)/(d)("Dividenod")i.e.(a)/(b)=(c)/(d)implies(a)/(b)-1=(c)/(d)-1 3. If a:b:=c:d, then (a+b)/(a-b)=(c+d)/(c-d)("Componendo and dividendo") If a/b=c/d=e/fand(2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(2b^(6)+3b^(2)d^(2)-5f^(5))=((a)/(b))^(n) then teh value of n is :

If a/b=c/d=e/f=9/5 then (2a + 3c + 5e)/( 2b + 3d + 5f) = ?

If a/b=c/d=e/f, then show that (a^(3)b+2c^(2)e-3ae^(2)f)/(b^(4)+2d^(2)f-3bf^(3))=(ace)/(bdf) (wherever defined)

If (a)/(2b) = (c )/(d) = (e )/(3f) , then the value of (2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(32b^(6)+12b^(2)d^(2)-405f^(5)) is

If (a)/(b)=(c)/(d)=(e)/(f)=3 , then (2a^2 + 3c^(2) + 4e^(2))/(2b^(2) + 3d^(2) + 4f^(2))=?

MOTION-BASIC MATHEMATIC & LOGARITHM -Exercise - 3
  1. Factorize 1 + x^(4) + x^(8)

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  2. Factorize x^(4) + 4

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  3. If a/b=c/d=e/f and (2a^4b^2+3a^2c^2-5e^4f)/(2b^6+3b^2d^2-5f^5)=(a/b)^n...

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  4. Which is greater log(2)3 " or " log(1//2) 5

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  5. Which is greater log(7) 11 " or " log(8) 5

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  6. Find the value oflog(1//3)root(4)(729*root(3)(9^(-1)*27^(-4//3))).

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  7. The value of a ^(logb (logb x)/(logb a)) is

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  8. Find the value of 4^(5log(4sqrt2)(3-sqrt6)-6log8(sqrt3-sqrt2)).

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  9. Compute the following (81^(1/((log)5 9))+3^(3/((log)(sqrt(6))3)))/(409...

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  10. 5^(log(1/5)(1/2)) +log(sqrt(2)) (4/(sqrt(7)+sqrt(3)))+log(1/2)(1/(10+2...

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  11. a) Calculate: 4^(5log(4sqrt(2))(3-sqrt(6))-6log(e)(sqrt(3)-sqrt(2))) ...

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  12. (a) Which is smaller ? 2 or (log(pi) 2 + log(2) pi). (b) Prove t...

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  13. Let A denotes the value of log10 {(ab+sqrt((ab)^2-4(a+b)))/2}+log10 {l...

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  14. Solve following log equation x^((logx+5)/3)=10^(5+logx)

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  15. If x, where 0,1,2 are respectively the values of x satisfying the equa...

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  16. log(4)(log(2)x)+log(2)(log(4)x)=2

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  17. Solve the equation 5^(x)root(x)(8^(x-1))=500

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  18. Given that log2(3)=a,log3(5)=b,log7(2)=c, express the logrithm of the ...

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

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  20. If (loga)/(b-c) = (logb)/(c-a) = (logc)/(a-b), then prove that a^(a)...

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