Home
Class 12
MATHS
The domain of f(x)=log5|log(e)x| , is...

The domain of `f(x)=log_5|log_(e)x|` , is

A

`(0,oo)`

B

`(1,oo)`

C

`(0,1) cup (1,oo)`

D

`(-oo,1)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the domain of the function \( f(x) = \log_5 |\log_e x| \), we need to ensure that the expression inside the logarithm is valid. Here are the steps to determine the domain: ### Step 1: Determine the condition for \( \log_e x \) The logarithm \( \log_e x \) is defined only for \( x > 0 \). Therefore, the first condition we have is: \[ x > 0 \]
Promotional Banner

Topper's Solved these Questions

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|94 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

Similar Questions

Explore conceptually related problems

The domain of f(x)=log|logx| is

The domain of definition of f(x)=log_(3)|log_(e)x| , is

If f(x)=|log_(e) x|,then

The domain of f(x) = log |x| + 1/sqrt|x| + 1/log|x| is R - A where A is set

Find the domain of f(x)=(log)_(10)(log)_2(log)_(2/pi)(t a n^(-1)x)^(-1)

Find domain of f(x)=log_(10)log_(10)(1+x^(3)) .

Domain of f(x) =log _((x))(9-x ^(2)) is :

If f is a real function, find the domain of f(x)=(1)/(log|x|)

Find the domain of f(x) = log (e^(x) - x) + (1)/(sqrt(5[x] - [x]^(2) - 6))

The domain of the function f(x)=log_2[log_3(log_4(x^2-3x+6)}]i s .

OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Chapter Test
  1. Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(...

    Text Solution

    |

  2. The domain of definition of the function f(x)=tan((pi)/([x+2])), is wh...

    Text Solution

    |

  3. The range of the function f(x)=sin [log (sqrt(4-x^(2))/(1-x)) is :

    Text Solution

    |

  4. The range of the function y=(x+2)/(x^2-8x-4)

    Text Solution

    |

  5. The range of the function f(x)=1+sinx+sin^(3)x+sin^(5)x+…… when x in ...

    Text Solution

    |

  6. The period of the function f(x)=|sin 3x|+| cos 3x| , is

    Text Solution

    |

  7. The function f(x)={{:( 1, x in Q),(0, x notin Q):}, is

    Text Solution

    |

  8. Which of the following functions has period pi ?

    Text Solution

    |

  9. The function f(x)=x[x] , is

    Text Solution

    |

  10. If f(x) and g(x) are periodic functions with the same fundamental per...

    Text Solution

    |

  11. The range of the function f(x)=cosec^(-1)[sinx] " in " [0,2pi], where ...

    Text Solution

    |

  12. If f(sinx)-f(-sinx)=x^(2)-1 is defined for all x in R , then the val...

    Text Solution

    |

  13. Let f:[pi,3pi//2] to R be a function given by f(x)=[sinx]+[1+sinx]+[2...

    Text Solution

    |

  14. Let the function f(x)=3x^(2)-4x+8log(1+|x|) be defined on the interval...

    Text Solution

    |

  15. If f:[-4,0]->R is defined by f(x) = e^x + sin x, its even extension to...

    Text Solution

    |

  16. Which one of the following is not periodic ?

    Text Solution

    |

  17. The domain of the function f(x)=(sin^(-1)(3-x))/(log(e)(|-x|-2)), is

    Text Solution

    |

  18. The domain of f(x)=log5|log(e)x| , is

    Text Solution

    |

  19. The period of sin^(2) theta , is

    Text Solution

    |

  20. f(x)=""^(16-x)C(2x-1)+""^(20-3x)P(4x-5)

    Text Solution

    |