Home
Class 8
MATHS
If 5^x=3^y=45^z, prove that 1/z=1/x+2/y....

If `5^x=3^y=45^z,` prove that `1/z=1/x+2/y.`

Promotional Banner

Topper's Solved these Questions

  • INDICES

    PEARSON IIT JEE FOUNDATION|Exercise CONCEPT APPLICATION (Level 1)|33 Videos

  • INDICES

    PEARSON IIT JEE FOUNDATION|Exercise CONCEPT APPLICATION (Level 2)|20 Videos

  • INDICES

    PEARSON IIT JEE FOUNDATION|Exercise Test Your Concepts (Very Short Answer Type Questions)|43 Videos

  • GEOMETRY

    PEARSON IIT JEE FOUNDATION|Exercise CONCEPT APPLICATION (Level 1)|60 Videos

  • LINEAR EQUATIONS AND INEQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise CONCEPT APPLICATION (LEVEL - 3)|9 Videos

Similar Questions

Explore conceptually related problems

5^(x)=3^(y)=15^(z), Prove that (1)/(z)=(1)/(x)+(1)/(y)

If 2^(x)=3^(y)=6^(-z) prove that (1)/(x)+(1)/(y)+(1)/(z)=0

If 3^(x)=5^(y)=45^(z), then a.(2)/(z)=(1)/(y)-(1)/(x)b(2)/(y)=(1)/(x)-(1)/(z)c*(2)/(x)=(1)/(z)-(1)/(y)dx+y+z=0

If x+y+z=xzy , prove that : (2x)/(1-x^2) + (2y)/(1-y^2) + (2z)/(1-z^2) = (2x)/(1-x^2) (2y)/(1-y^2) (2z)/(1-z^2)

If x+y+z=xyz prove that (2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(2x)/(1-x^(2))(2y)/(1-y^(2))(2z)/(1-z^(2))

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

If xy+yz+xz=1, then prove that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If x,y,z gt 0 then prove that (x+y+z)(1/x+1/y+1/z) geq 9

PEARSON IIT JEE FOUNDATION-INDICES-Test Your Concepts (Short Answer Type Questions)
  1. Simplify (5(81)^(n+1)-3^(4n+5))/(3xx3^(4n)+(81)^n).

    Text Solution

    |

  2. (1) If 5^(n+2)=625 ,f i n d[(n+3)]^(1/3): (2) If (32/243)^n=8/27 ,f i...

    Text Solution

    |

  3. If ((32)/(243))^(n)= (8)/(27), then find ((n+0.4)/(1024))^(-n)

    Text Solution

    |

  4. simplify (2^(2/3)-2^(- 2/3))(2^(4/3)+1+2^(- 4/3))

    Text Solution

    |

  5. (i) Simplify (2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3)) (ii) [(root(...

    Text Solution

    |

  6. If 16200=2^(a)xx3^(b)xx^(c), then find a, b, c.

    Text Solution

    |

  7. Simplify ((p^(a))/(p^(b))) xx ((p^(b))/(p^(c ))) xx ((p^(c ))/(p^(a)))...

    Text Solution

    |

  8. If [root(9)((2/3)^5)]^(sqrt(x-5)) = a^0, find the value of x.

    Text Solution

    |

  9. Simplify ((p^(a+b))^(5).(p^(b+c))^(5).(p^(c+a))^(5))/((p^(a). p^(b). p...

    Text Solution

    |

  10. If 5^(3x+2)=25xx5^((4x-1)), find the value of x.

    Text Solution

    |

  11. Which of the following is greater between each of the two numbers ? ...

    Text Solution

    |

  12. Which of the following is greater between each of the two numbers ? ...

    Text Solution

    |

  13. Which of the following is greater between each of the two numbers ? ...

    Text Solution

    |

  14. If 5^x=3^y=45^z, prove that 1/z=1/x+2/y.

    Text Solution

    |

  15. Prove that 1/(1+p+q^(- 1))+1/(1+q+r^(- 1))+1/(1+r+p^(- 1))=1,if pqr=1 ...

    Text Solution

    |

  16. ((a+b+c)^(a+b)(a+b+c)^(b+c)(a+b+c)^(c+a))/([(a+b+c)^(a) (a+b+c)^(b) (a...

    Text Solution

    |

  17. Simplify the given expressions (a^(p+q))^(p-q) (a^(q+r))^(q-r) (a^(r...

    Text Solution

    |

  18. [(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt...

    Text Solution

    |

  19. Prove that ((x^(-1)+y^(-1))/x^(-1))^(-1)+((x^(-1)-y^(-1))/x^(-1))^(...

    Text Solution

    |

  20. If a, b, c are real numbers, then show that root(5)(ab^-1)xxroot( 5)...

    Text Solution

    |