Home
Class 12
MATHS
The number of real solutions of the (log...

The number of real solutions of the `(log)_(0. 5)|x|=2|x|` is (a) 1 (b) 2 (c) 0 (d) none of these

A

1

B

2

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

Draw the graph of `y=log_(0.5)|x| " and " y=2|x|.`

Clearly, from the graph, there are two solutions.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos
  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos
  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos
  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the number of real solutions to the equation log_(0.5)x=|x| .

The number of real solution of the equation x^(2)-3|x|+2=0 is

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

The number of real or complex solutions of x^(2)-6|x|+8=0 is

If a ,b ,c are three distinct positive real numbers, the number of real and distinct roots of a |x^2|+2b|x|-c=0 is a. 0 b. 4 c. 2 d. none of these

The total number of solution of cosx=sqrt(1-sin2x) in [0,2pi] is equal to 2 (b) 3 (c) 5 (d) none of these

The number of solutions of the equation log_(x+1)(x-0.5)=log_(x-0.5)(x+1) is

The number of solutions of sqrt(3x^(2)+x+5)=x-3 is (A) 0 (B) 1 (C) 2 (D) 4

Which of the following is not the solution of (log)_x(5/2-1/x)> 1 (a)( 2/5,1/2) (b) (1,2) (c) (2/5 , 1) (d) Non of these

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

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The domain of the function f(x)=sqrt(log(1/(|sinx|))) R-{-pi,pi} (b)...

    Text Solution

    |

  2. Domain of definition of the function f(x) = log2 (-log(1/2) (1+x^(-4))...

    Text Solution

    |

  3. The number of real solutions of the (log)(0. 5)|x|=2|x| is (a) 1 (b) ...

    Text Solution

    |

  4. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

    Text Solution

    |

  5. The domain of the function f(x)=sqrt("In"((|x|-1))(x^(2)+4x+4)) is

    Text Solution

    |

  6. The domain of f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,...

    Text Solution

    |

  7. The domain of the function f(x)=1/(sqrt(4x=|x^2-10 x+9})) is (7-sqrt(...

    Text Solution

    |

  8. The domain of the function f(x)=(1)/(sqrt(|cosx|+cosx)) is

    Text Solution

    |

  9. The exhaustive domain of the following function is f(x)=sqrt(x^(12)-x^...

    Text Solution

    |

  10. The number of integral values of x for which the function sqrt(sinx+co...

    Text Solution

    |

  11. 29. Which one of following best represents the graph of y=x^(logx pi)

    Text Solution

    |

  12. If x is real, then the value of the expression (x^2+14 x+9)/(x^2+2x+3)...

    Text Solution

    |

  13. The range of the function f(x)=|x-1|+|x-2|, -1 le x le 3, is

    Text Solution

    |

  14. The function f: R-R is defined by f(x)=cos^2x+sin^4xforx in Rdot Then...

    Text Solution

    |

  15. The range of f9x)=[|s in x|+|cosx"|""]"dot Where [.] denotes the great...

    Text Solution

    |

  16. The range of function f(x)=^(7-x)P(x-3)i s {1,2,3} (b) {1,2,3,4,5,...

    Text Solution

    |

  17. The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is [0,pi/2] (b) (0,pi/6) ...

    Text Solution

    |

  18. The range of the function f(x)=(e^x-e^(|x|))/(e^x+e^(|x|)) is (a)(-oo,...

    Text Solution

    |

  19. Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] deno...

    Text Solution

    |

  20. The range of the function f defined by f(x)=[1/(sin{x})] (where [.] an...

    Text Solution

    |