Home
Class 12
MATHS
The value of x satisfying the equation 3...

The value of `x` satisfying the equation `3sqrt(5)^(log)_5 5^(((log)_5(log)_5log_5(x/2)))` 1 (b) 3 (c) 18 (d) 54

A

1

B

3

C

18

D

54

Text Solution

Verified by Experts

The correct Answer is:
D
Using ` a^(log_(a)N) = N` repeatedly, we get
`(root(3)5)^(log _(5)(x/2)) = 3`
`rArr 5^(log_(5)(x/2)^(1//3)) = 3`
`rArr (x/2)^(1//3)= 3`
` rArr x/2 = 27`
`rArr x = 54`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The value of x satisfying the equation 3sqrt(5)^((log_5) 5^(((log)_5(log)_5log_5(x/2))) = 3 1 (b) 3 (c) 18 (d) 54

The value of x satisfying sqrt3^(-4+2log_(sqrt5)x)= 1//9 is

The value of x for which the equation 5*3^(log_3x)-2^(1-log_2x)-3=0

Number of real values of x satisfying the equation log_2(x^2-x)*log_2((x-1)/x)+(log_2x)^2=4 ,is (a) 0 (b) 2 (c) 3 (d) 7

The values of x, satisfying the equation for AA a > 0, 2log_(x) a + log_(ax) a +3log_(a^2 x)a=0 are

The number of integers satisfying the inequality log_(sqrt(0.9))log_(5)(sqrt(x^(2)+5+x))gt 0 is

Find the number of solution to equation (log)_2(x+5)=6-x :

Integral value of x which satisfies the equation =log_6 54+(log)_x 16=(log)_(sqrt(2))x-(log)_(36)(4/9)i s ddot

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

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx) is (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y)...

    Text Solution

    |

  2. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

    Text Solution

    |

  3. The value of x satisfying the equation 3sqrt(5)^(log)5 5^(((log)5(log)...

    Text Solution

    |

  4. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals odd integer (b)...

    Text Solution

    |

  5. if (log)y x+(log)x y=1,x^2+y=12 , the value of x y is 9 (b) 12 (c) 15 ...

    Text Solution

    |

  6. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

    Text Solution

    |

  7. If (x+1)^((log)(10)(x+1))=100(x+1), then

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |