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Solve : 6((log)x2-(log)4x)+7=0....

Solve : `6((log)_x2-(log)_4x)+7=0.`

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`6(log_x2 - log_4x)+7 = 0`
`=>6(log_2 2/(log_2 x) - log_2x/log_2 4) +7 = 0`
`=>6(1/(log_2 x) - log_2x/2) +7 = 0`
Let `log_2x =t`, then our equation becomes,
`=>6(1/t - t/2)+7 =0`
`=>12-6t^2+14t = 0`
`=>3t^2- 7t -6 =0`
`=>3t^2- 9t + 2t -6 =0`
...
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CENGAGE PUBLICATION-LOGARITHM-All Questions
  1. Solve : (log)(0. 3)(x^2-x+1)>0

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  2. Solve 1<(log)2(x-2)lt=2.

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  3. Solve : 6((log)x2-(log)4x)+7=0.

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  4. Solve 4^(log(2)log(x))=logx-(logx)^(2)+1 (base is e).

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  5. Solve: 4(log)(x/2)(sqrt(x))+2(log)(4x)(x^2)=3(log)(2x)(x^3)dot

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  6. Solve 4^((log)9x)-6x^((log)9 2)+2^((log)3 27)=0

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  7. Solve: 1/4x^(log2sqrt(x))=(2. x^((log2x)))^(1/4)dot

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  8. Solve |x-1|^((log(10) x)^2-log(10) x^2=|x-1|^3

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  9. Solve (log)2(x-1)> 4.

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  10. Solve (log)3(x-2)lt=2.

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  11. If x1a n dx2 are the roots of the equation e^2 x^(lnx)=x^3 with x1> x2...

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  12. If x y^2=4a n d(log)3((log)2x)+(log)(1/3)((log)(1/2)y)=1,t h e nxe q u...

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  13. x^((log)5x)>5 implies x in (0,oo) (b) [2,2.5] (c) (2,2.5) (d) (0,2...

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  14. The number of real values of the parameter k for which (log(16)x)^2-(l...

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  15. If S={x in R :((log)(0. 6)0. 216)(log)5(5-2x)lt=0}, then S is equal t...

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  16. If S={x in N :2+(log)2sqrt(x+1)>1-(log)(1/2)sqrt(4-x^2)} , then S={1...

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  17. Equation (log)4(3-x)+(log)(0. 25)(3+x)=(log)4(1-x)+(log)(0. 25)(2x+1)h...

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  18. Solution set of the inequality 1/(2^x-1)>1/(1-2^(x-1)) is 1,oo) (b) 0...

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  19. The solution set of the inequality (log)(10)(x^2-16)lt=(log)(10)(4x-11...

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  20. Which of the following is a solution of (logx)(5/2-1/x) gt (5/2-1/x) ?

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