Home
Class 11
MATHS
If (log)k xdot(log)5k=(log)x5,k!=1,k >0,...

If `(log)_k xdot(log)_5k=(log)_x5,k!=1,k >0,` then `x` is equal to (a)`k` (b) 1/5 (c) 5 (d) none of these

Text Solution

Verified by Experts

`log_y^x=log_c^x/log_c^y`
`(logx/logk)*(logk/log5)=log5/logx`
`(logx)^2=(log5)^2`
`logx=log5`
`x=5`.
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE|Exercise Solved Examples And Exercises|63 Videos
  • PERMUTATIONS AND COMBINATIONS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

Similar Questions

Explore conceptually related problems

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

The number of real values of the parameter k for which (log_(16)x)^2-(log)_(16)x+(log)_(16)k=0 with real coefficients will have exactly one solution is (1) 2 (b) 1 (c) 4 (d) none of these

If (log_2x)/4=(log_2y)/6=(log_2z)/(3k) and x^3 y^2 z=1 , then k is equal to

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1 ,then x equals (a) 4 (b) 8 (c) 16 (d) 64

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

If a gt 1, x gt 0 and 2^(log_(a)(2x))=5^(log_(a)(5x)) , then x is equal to

CENGAGE-LOGARITHM-Solved Examples And Exercises
  1. Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) ...

    Text Solution

    |

  2. The real solutions of the equation 2^(x+2). 5^(6-x)=10^x^2 is/are 1 (b...

    Text Solution

    |

  3. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to (a)k ...

    Text Solution

    |

  4. If p , q in N satisfy the equation x^sqrt(x)=(sqrt(x))^x, then pa n...

    Text Solution

    |

  5. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is )

    Text Solution

    |

  6. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

    Text Solution

    |

  7. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

    Text Solution

    |

  8. Solve the following equation of x :2(log)x a+(log)(a x)a+3(log)(a^2x)a...

    Text Solution

    |

  9. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

    Text Solution

    |

  10. Which of the following, when simplified, reduces to unity? (a) (log)(...

    Text Solution

    |

  11. If (log)a x=b for permissible values of a and x , then identify the ...

    Text Solution

    |

  12. The number of positive integers satisfying x+(log)(10)(2^x+1)=x(log)(1...

    Text Solution

    |

  13. Solve: ((1/2)^(log(10)a^2) +2>3/(2^((log)(10)(-a))))

    Text Solution

    |

  14. Write the characteristic of each of the following numbers by using t...

    Text Solution

    |

  15. Solve: (log)2((x^2+1)/(x-1))<0

    Text Solution

    |

  16. Solve: (x-1)/((log)3(9-3^x)-3)lt=1.

    Text Solution

    |

  17. Find the mantissa of the logarithm of the number 0.002359

    Text Solution

    |

  18. Use the logarithm tables to find the logarithm of the following number...

    Text Solution

    |

  19. Write the significant digits in each of the following numbers to co...

    Text Solution

    |

  20. Find the mantissa of the logarithm of the number 5395

    Text Solution

    |