Home
Class 11
MATHS
If y^2=x z and a^x=b^y=c^z , then prove...

If `y^2=x z and a^x=b^y=c^z ,` then prove that `(log)_ab=(log)_bc`

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE ENGLISH|Exercise All Questions|444 Videos

Similar Questions

Explore conceptually related problems

If x, y, z are in G.P. and a^x=b^y=c^z , then (a) logba=log_ac (b) log_cb =log_ac (c) log_ba=log_cb (d) none of these

If a^x=b^y=c^z=d^w then log_a(bcd)=

If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)

If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)

If y=a^(x^(a^x..oo)) then prove that dy/dx=(y^2 log y )/(x(1-y log x log y))

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If y=a^(1/(1-(log)_a x)) and z=a^(1/(1-(log)_a y)) ,then prove that x=a^(1/(1-(log)_a z))

If y log x= x-y , prove that (dy)/(dx)= (log x)/((1+log x)^(2))

CENGAGE ENGLISH-LOGARITHM-All Questions
  1. Find the value of (1/(49))^(1+(log)7 2)+5^(-1(log)((1/5))(7))

    Text Solution

    |

  2. Prove that: 2^((sqrt((log)a4sqrt(a b)+(log)b4sqrt(a b))-sqrt((log)a4sq...

    Text Solution

    |

  3. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

    Text Solution

    |

  4. Solve (log)4 8+(log)4(x+3)-(log)4(x-1)=2.

    Text Solution

    |

  5. Which of the following pairs of expression are defined for the same se...

    Text Solution

    |

  6. Solve (log)2(3x-2)=(log)(1/2)x

    Text Solution

    |

  7. Solve log(-x)=2log(x+1)dot

    Text Solution

    |

  8. Solve: (log)2(4.3^x-6)-(log)2(9^x-6)=1.

    Text Solution

    |

  9. Solve 2^(x+2)27^(x//(x-1))=9

    Text Solution

    |

  10. Suppose x , y ,z=0 and are not equal to 1 and logx+logy+logz=0. Find t...

    Text Solution

    |

  11. If (log)(12)27=a , then find (log)6 16int e r m sofa

    Text Solution

    |

  12. If y^2=x z and a^x=b^y=c^z , then prove that (log)ab=(log)bc

    Text Solution

    |

  13. Simplify: 1/(1+(log)a b c)+1/(1+(log)b c a)+1/(1+(log)c a b)

    Text Solution

    |

  14. If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

    Text Solution

    |

  15. Find the value of ((log)3 4)((log)4 5)((log)5 6)((log)6 7)((log)7 8)((...

    Text Solution

    |

  16. y=2^(1/((log)x4), then find x in terms of y.

    Text Solution

    |

  17. If n >1,t h e np rov et h a t 1/((log)2n)+1/((log)3n)++1/((log)(53)n)...

    Text Solution

    |

  18. What is logarithm of 32 root(5) 4" to the base "2sqrt2?

    Text Solution

    |

  19. Which is greater: x=(log)3 5ory=(log)(17)25 ?

    Text Solution

    |

  20. The product of roots of the equation (3)/((log8x)^2)=3 is 1 (b) (c)...

    Text Solution

    |