Home
Class 9
MATHS
Find the value of (yz)^(log y - log z) x...

Find the value of `(yz)^(log y - log z) xx (zx)^(log z - log x) xx (xy)^(log x - log y)`.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Examples (Short-answer type questions)|1 Videos

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Examples (Long-answer type question)|25 Videos

  • LINEAR EQUATIONS IN REAL PROBLEMS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-5|31 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.4|52 Videos

Similar Questions

Explore conceptually related problems

Prove that x^(log y - logz) xx y^(log z - logx) xx z^(log x - log y) = 1 .

Find the range of f(x)=(log)_e x-((log)_e x)^2/(|(log)_e x|)

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3- (log)_3 2 (c) log(3/2) (d) none of these

Prove that : (iii) (yz)^(log(y/z))(zx)^(log(z/x))(xy)^(log(x/y)) = 1

Find the values : (log_(a)b)xx(log_(b)c)xx(log_(c )d)xx(log_(d)a)

y = c log x - 2

If x, y and z be greater than 1, then the value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)| is

int (dx)/(x log x[log (log x)])

Find (dy)/(dx) , when y=(x log x)^(log(logx))

CALCUTTA BOOK HOUSE-LOGARITHM-Exercise - 7 (Long-answer type questions)
  1. Find the value of (yz)^(log y - log z) xx (zx)^(log z - log x) xx (xy)...

    Text Solution

    |

  2. Calculate : (i) log(2)root(4)(64root(3)(4^(-1)(8)^(-4/3)))

    Text Solution

    |

  3. Calculate : (ii) log(5)sqrt(5sqrt(5sqrt(5....................oo)))

    Text Solution

    |

  4. Calculate : (iii) log(3)(sqrt6)+log(3)(sqrt(2/3))-log(3)log(3)(9)

    Text Solution

    |

  5. Calculate : (iv) 2log(2)sqrt(2sqrt(2sqrt(2....................oo)))

    Text Solution

    |

  6. Calculate : (v) 1/6 sqrt((3log 1728)/(1+1/2 log 0.36 + 1/3log8))

    Text Solution

    |

  7. Calculate : (vi) log(2)5 xx log(6)16 xx log(5) 8 xx log(8)6.

    Text Solution

    |

  8. Simplify : (i) log(1/(sqrtx) )(y) xx log(1/(root(3)(y)))(z) xx log(1...

    Text Solution

    |

  9. Simplify : (ii) 23 log 16/15 + 17log 25/24 + 10log 81/80

    Text Solution

    |

  10. Simplify : (iii) 3log((36)/(25))+log((6)/(27))^(3)-2log((16)/(125))

    Text Solution

    |

  11. Prove that log2+16log (16/15)+12log(25/24)+7log(81/80)=1

    Text Solution

    |

  12. If log(40)4 = a and log(40)5 = b, then show that log(40)16=4(1-a-b).

    Text Solution

    |

  13. If log(6)15 = alpha, log(12)18= beta and log(25)24 = gamma, then prove...

    Text Solution

    |

  14. If log(12)18 = x and log(24)54 = y, then show that xy + 5(x-y) = 1

    Text Solution

    |

  15. If log(a)M = (logb M) xx P, then express P in terms of a and b.

    Text Solution

    |

  16. If 1/2 log(3)M + 3log(3)N = 1, then express M in terms of N.

    Text Solution

    |

  17. Prove that 1/(log2 pi) + 1/(log(6)pi) > 2.

    Text Solution

    |

  18. Prove that the value of log(10)3 lies in between 1/2 and 2/5.

    Text Solution

    |

  19. Prove that the value of log(20)3 lies in between 1/2 and 1/3.

    Text Solution

    |

  20. Prove that : (i) log(1^(1/5)+32^(1/5)+243^(1/5))=1/5(log1 + log 32 +...

    Text Solution

    |

  21. Prove that : (ii) log(1+2+3) = log1 + log2 + log3.

    Text Solution

    |