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If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1...

If `(log)_(10)[1/(2^x+x-1)]=x[(log)_(10)5-1]` , then `x=` 4 (b) 3 (c) 2 (d) 1

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
R.H.S. = `x=[log_(10) 5-log_(10)10]=x log_(10). 5/10 = log_(10).(1)/2^(x)`
` rArr 1/(2^(x)+x-1)=1/2^(x)`
Therefore ` x - 1 = 0 or x = 1`.
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If (x+1)^((log)(10)(x+1))=100(x+1), then

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  2. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

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  3. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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  4. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

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  5. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to 2 (b) 4 (c) 8 (d...

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  6. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

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  7. The value of b for which the equation 2(log)(1/(25))(b x+28)=-(log)5(1...

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  8. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

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  9. The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d...

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  10. The product of roots of the equation (log8(8/x^2))/((log8x)^2)=3 is 1 ...

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  11. Let a >1 be a real number. Then the number of roots equation a^(2(log)...

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  12. The number of roots of the equation (log)(3sqrt("x"))x+(log)(3x)sqrt(x...

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  13. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

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  14. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

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  15. Find the value of x satisfying the equations log(3)(log(2)x)+log(1//3)...

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

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

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

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  19. 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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  20. 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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