Home
Class 12
MATHS
The total number of solutions of loge |s...

The total number of solutions of `log_e |sin x| = -x^2 +2x in [0,pi]` is equal to

A

1

B

2

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`log_(e)|sin x|=-x(x-2)`
Graphs of `y=log_(e)|sin x|` and `y=-x(x-2)` meet exactly two times in `[0, pi]`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.9|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

The total number of solutions of cos x= sqrt(1- sin 2x) in [0, 2pi] is equal to

Number of solutions of e log_(e)x=x is

Total number of solutions of tan x + cot x=2cosec x in [-2pi,2pi] is equal to

The tatal number of solutions of ln|sin x|=-x^(2)+2x in[-(pi)/(2),(3 pi)/(2)] is equal to

The total number of solutions of sin(pi x)=|log|x||is|

Find the total number of solutions of sin pi x=|ln|x|

The total number of solution of |cot x|=cot x+(1)/(sin x),x in[0,3 pi], is equal to 1(b)2(c)3(d)0

Total number of solutions of sin^(4)x+cos^(4)x=sinx*cosx in [0,2pi] is equal to

Find the total number of solution of sin^(4)x+cos^(4)x=sinxcosx" in "[0,2pi] is equal to

Total number of solutions of 2^(cos x)=|sin x| in [-2 pi,5 pi]

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. The general solution of the equation sin^100 x - cos^100 x =1 is (wher...

    Text Solution

    |

  2. The sum of all the solutions in [0, 4pi] of the equation tan x+ cot x+...

    Text Solution

    |

  3. The total number of solutions of loge |sin x| = -x^2 +2x in [0,pi] is...

    Text Solution

    |

  4. The total number of solution of sin{x}=cos{x} (where {} denotes the fr...

    Text Solution

    |

  5. The set of all xin((-pi)/2,pi/2) satisfying |4sinx-1|<sqrt(5) is given...

    Text Solution

    |

  6. If roots of the equation 2x^2-4x+2sintheta-1=0 are of opposite sign, t...

    Text Solution

    |

  7. If |2 sin theta-cosec theta| ge 1 and theta ne (n pi)/2, n in Z, then

    Text Solution

    |

  8. Which of the following is not the solution of the equation sin 5x=16 s...

    Text Solution

    |

  9. The number of solutions of the equation |2 sin x-sqrt(3)|^(2 cos^(2)...

    Text Solution

    |

  10. One root of the equation cos x-x+1/2=0 lies in the interval (A...

    Text Solution

    |

  11. The smallest positive x satisfying the equation (log)(cosx)sinx+(log)(...

    Text Solution

    |

  12. The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+...

    Text Solution

    |

  13. Consider the system of linear equations in x, y, and z: (sin 3 theta...

    Text Solution

    |

  14. The equation sin^4x-2cos^2x+a^2=0 can be solved if -sqrt(3)lt=alt=sqrt...

    Text Solution

    |

  15. If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then...

    Text Solution

    |

  16. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

    Text Solution

    |

  17. The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where...

    Text Solution

    |

  18. The equation cos^8 x + b cos^4 x + 1 = 0 will have a solution if b be...

    Text Solution

    |

  19. The number of values of yin[-2pi,2pi] satisfying the equation |sin2x|+...

    Text Solution

    |

  20. If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi]...

    Text Solution

    |