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Prove that (2^((log)2 1/4x)-3^((log)(27...

Prove that `(2^((log)_2 1/4x)-3^((log)_(27)(x^2+1)^3)-2x) /(7^(4(log)_(49)x)-x-1)>0`

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To prove that \[ \frac{2^{\log_2 \left(\frac{1}{4}x\right)} - 3^{\log_{27} \left((x^2 + 1)^3\right)} - 2x}{7^{4\log_{49} x} - x - 1} > 0, \] we will simplify the expression step by step. ...
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CENGAGE ENGLISH-LOGARITHM-All Questions
  1. Find the value of (1/(49))^(1+(log)7 2)+5^(-1(log)((1/5))(7))

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  2. Prove that: 2^((sqrt((log)a4sqrt(a b)+(log)b4sqrt(a b))-sqrt((log)a4sq...

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  3. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

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  4. Solve (log)4 8+(log)4(x+3)-(log)4(x-1)=2.

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  5. Which of the following pairs of expression are defined for the same se...

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  6. Solve (log)2(3x-2)=(log)(1/2)x

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  7. Solve log(-x)=2log(x+1)dot

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  8. Solve: (log)2(4.3^x-6)-(log)2(9^x-6)=1.

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  9. Solve 2^(x+2)27^(x//(x-1))=9

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  10. Suppose x , y ,z=0 and are not equal to 1 and logx+logy+logz=0. Find t...

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  11. If (log)(12)27=a , then find (log)6 16int e r m sofa

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  12. If y^2=x z and a^x=b^y=c^z , then prove that (log)ab=(log)bc

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  13. Simplify: 1/(1+(log)a b c)+1/(1+(log)b c a)+1/(1+(log)c a b)

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  14. If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

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  15. Find the value of ((log)3 4)((log)4 5)((log)5 6)((log)6 7)((log)7 8)((...

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  16. y=2^(1/((log)x4), then find x in terms of y.

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  17. If n >1,t h e np rov et h a t 1/((log)2n)+1/((log)3n)++1/((log)(53)n)...

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  18. What is logarithm of 32 root(5) 4" to the base "2sqrt2?

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  19. Which is greater: x=(log)3 5ory=(log)(17)25 ?

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  20. The product of roots of the equation (3)/((log8x)^2)=3 is 1 (b) (c)...

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