Home
Class 11
MATHS
If p,q in N" satisfy the equation "x^(s...

If `p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x)`, then

Text Solution

Verified by Experts

`x^sqrtx=sqrtx^x`
taking log both side
`sqrtxlogx=xlogsqrtx`
`sqrtxlogx=x/2logx`
`sqrtxlogx-x/2logx=0`
`logx[sqrtx-x/2]=0`
either log x=0
`x=1`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE PUBLICATION|Exercise All Questions|430 Videos

Similar Questions

Explore conceptually related problems

The roots of the equation x^sqrtx=sqrt(x^x) are

Integrate the functions (cossqrtx)/(sqrtx)

(-1) is a root of the equation sqrtx+(1)/(sqrtx)=2 .

The highest power of the variable of the equation sqrtx-(1)/(sqrtx)=a^(2) (a= constant) is 2.

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

Integrate the functions 1/(x-sqrtx)

If x + 7 + 4 sqrt3 , then sqrtx + (1)/(sqrtx) = 4

int dx/(x+sqrtx) is equal to

int(cossqrtx)/sqrtx dx =

CENGAGE PUBLICATION-LOGARITHM-All Questions
  1. The real solutions of the equation 2^(x+2). 5^(6-x)=10^(x^2) is/are 1 ...

    Text Solution

    |

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

    Text Solution

    |

  3. If p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x), then

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Which of the following, when simplified, reduces to unity?

    Text Solution

    |

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

    Text Solution

    |

  11. The value of x satisfying x+log10(1+2^x)=x log10 5+log10 6 is

    Text Solution

    |

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

    Text Solution

    |

  13. Write the characteristic of each of the following numbers by using ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |