Home
Class 12
MATHS
Prove that a^x-b^y=0\ w h e r e\ x="\ "s...

Prove that `a^x-b^y=0\ w h e r e\ x="\ "sqrt(("log")_a b)\ &\ y=sqrt((log)_b a\ ),\ a >0,\ b >0\ &\ a ,\ b!=1`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Prove that a^(x)-b^(y)=0 where x=sqrt(log_(a)(b)&y)=sqrt(log_(b)(a)),a>0,b>0&a,b!=1

prove that a^(x)-b^(y)=0 where x=sqrt(log_(a)b) and y=sqrt(log_(b)a),a>0,b>0 and a,b!=1

The value of a^(sqrt((log)_a b))-b^(sqrt((log)_b a))(w h e r ea ,b >0a n da , b!=1) is equal to...........

Prove that a sqrt(log_(a)b)-b sqrt(log_(b)a)=0

If a^x=b , b^y=c ,c^z=a and x=(log)_b a^2; y=(log)_c b^3& z=(log)_a c^k , where a,b, c >0 & a , b , c!=1 then k is equal to a.1/5 b. 1/6 c.(log)_(64)2 d. (log)_(32)2

Solve the system the equations (a x)^(loga)=(b y)^(logb); b^(logx)=a^(logy) w h e r e a >0, b >0a n d a!=b , a b!=1

If y^(2)=xz and a^(x)=b^(y)=c^(z), then prove that (log)_(a)b=(log)_(b)c

Comprehension 1 Let a^((log)_b x)=c w h e r e a , b , c & x are parameters. On the basis of above information, answer the following questions: If a=2 x=a^((log)_5 25)& c=sqrt(2) , then b is- a.2 b. 16 c. 12 d. 2

Prove that: log_(a)x xx log_(b)y=log_(b)x xx log_(a)y

RESONANCE DPP-JEE MAINS-All Questions
  1. If x=prod(n=1)^(2000)n , then the value of the expression, 1/(1/((log...

    Text Solution

    |

  2. Which of the folowing stotements ure true ? (i) The set of all rectang...

    Text Solution

    |

  3. Prove that a^x-b^y=0\ w h e r e\ x="\ "sqrt(("log")a b)\ &\ y=sqrt((lo...

    Text Solution

    |

  4. Which of the following is greater? 9/(sqrt(11)-sqrt(2)),9/(3sqrt(3))

    Text Solution

    |

  5. If A1, A2 be two A.M. and G1, G2 be two G.M.s between aa n db ...

    Text Solution

    |

  6. Which of the following are sets? Justify your answer. (i)  The coll...

    Text Solution

    |

  7. The solution of the equation 7^(logx)-5^(logx+1)=3. 5^(logx-1)-13. 7^(...

    Text Solution

    |

  8. Write the following sets in the tabular from : (i) A={x:x is a posit...

    Text Solution

    |

  9. If the first and (2n-1)^(th) terms of an A.P, a G.P and an H.P of posi...

    Text Solution

    |

  10. The number of integral value of x satisfying the following system of i...

    Text Solution

    |

  11. Write the following sets in the tabular from : (i) A={x:x is a posit...

    Text Solution

    |

  12. Solve the following equation for x: 9^(log3(log2x))=log2 x- (log2 x)^2...

    Text Solution

    |

  13. If |x3-2 2-3 1 1 3-2|=0t h e nxi s 1 b. 2 c.-3 d. -1

    Text Solution

    |

  14. Write the following sets in the tabular from : (i) A={x:x is a posit...

    Text Solution

    |

  15. Let a1, a2, a3, ,an be in G.P. such that 3a1+7a2+3a3-4a5=0. Then co...

    Text Solution

    |

  16. The ratio of the greatest value of 2-cos x+s in^2x to its least value ...

    Text Solution

    |

  17. Write the following sets in the tabular form: D={x : x is an letter of...

    Text Solution

    |

  18. Sum of the series 1/(4. 1^2-1)+1/(4. 2^2-1)+1/(4. 3^2-1)+ upto inf...

    Text Solution

    |

  19. The value of k for which product of two of the roots of the equation ...

    Text Solution

    |

  20. Write the following sets in the tabular form: E={x : x is a natural nu...

    Text Solution

    |