Home
Class 12
MATHS
The solution of the equation 5^(log(a)...

The solution of the equation
`5^(log_(a)x)+5x^(log_(a)5)=3, a gt0`, is

A

`5^(log_(a)5)`

B

`2^(-log5a)`

C

`2^(-log_(a)5)`

D

`2^(log5 a)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`5^(log_(a)x)+5x^(log_(a)5)=3`
`implies x^(log_(a)5)+5.x^(log_(a)5)=3" "[:'x^(logay)=y^(log_(a)x)]`
`implies 6x^(log_(a)5)=3 implies x^(log_(a)5)=(1)/(2) impliesx=2^(-log_(5)a)`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos

Similar Questions

Explore conceptually related problems

If 0 lt a lt 1 , then the solution set of the inequation (1+(log_(a)x)^(2))/(1+(log_(a)x)) gt1 , is

If x_1 and x_2 (x_2gtx_1) are the integral solutions of the equation (log_5x)^2+log_(5x)(5/x)=1 , , the value of |x_2-4x_1| is

Let x_(1) and x_(2) be two solutions of the equalition log_(x)(3x^(log_(5)x)+4) = 2log_(5)x , then the product x_(1)x_(2) is equal to

Solve the equation log_((log_(5)x))5=2

The number of solutions of the equation 5^x+5^-x=log_(10) 25, x in R is

The number of solutions of the equation log_(3)(3+sqrt(x))+log_(3)(1+x^(2))=0 , is

The solution set of the inequation log_(1//3)(x^(2)+x+1)+1 gt 0 , is

The solution of the equation (log)_7(log)_5(sqrt(x+5)+sqrt(x)=0 is...

The number of solutions of the equation log_(x+1)(x-0.5)=log_(x-0.5)(x+1) is

If x_(1) and x_(2) are solution of the equation log_(5)(log_(64)|x|+(25)^(x)-(1)/(2))=2x , then

OBJECTIVE RD SHARMA ENGLISH-MISCELLANEOUS EQUATIONS AND INEQUATIONS -Chapter Test
  1. The solution of the equation 5^(log(a)x)+5x^(log(a)5)=3, a gt0, is

    Text Solution

    |

  2. If 3^(x)+2^(2x) ge 5^(x), then the solution set for x, is

    Text Solution

    |

  3. The number of real solutions of the equation 1-x=[cosx] is

    Text Solution

    |

  4. The number of solutions of [sin x+cos x]=3+[-sin x]+[-cos x] in the ...

    Text Solution

    |

  5. Let x=(a+2b)/(a+b) and y=(a)/(b), where a and b are positive integers....

    Text Solution

    |

  6. The solution set contained in Rof the following inequation3^x+3^(1-x)...

    Text Solution

    |

  7. If 0lt x lt pi//2 and sin^(n) x+ cos^(n) x ge 1 , then

    Text Solution

    |

  8. The number of real roots of the equation x^(2)+x+3+2 sin x=0, x in [...

    Text Solution

    |

  9. The number of real roots of the equation 1+3^(x//2)=2^(x), is

    Text Solution

    |

  10. Total number of solutions of the equation sin pi x=|ln(e)|x|| is :

    Text Solution

    |

  11. The number of roots of the equation [sin^(-1)x]=x-[x], is

    Text Solution

    |

  12. The number of values of a for which the system of equations 2^(|x|)+|x...

    Text Solution

    |

  13. The number of real solutions (x, y, z, t) of simultaneous equations 2y...

    Text Solution

    |

  14. If the sum of the greatest integer less than or equal to x and the lea...

    Text Solution

    |

  15. If x,y and z are real such that x+y+z=4, x^(2)+y^(2)+z^(2)=6, x belong...

    Text Solution

    |

  16. Consider the equation : x^(2)+198x+30=2sqrt(x^(2)+18x+45)

    Text Solution

    |

  17. x^(8)-x^(5)-(1)/(x)+(1)/(x^(4)) gt 0, is satisfied for

    Text Solution

    |

  18. The number of solutions of the equation ((1+e^(x^(2)))sqrt(1+x^(2)))...

    Text Solution

    |

  19. The number of real roots of the equation 1+a(1)x+a(2)x^(2)+………..a(n)...

    Text Solution

    |

  20. Let a,b be integers and f(x) be a polynomial with integer coefficients...

    Text Solution

    |

  21. Let Pn(ix) =1+2x+3x^2+............+(n+1)x^n be a polynomial such that...

    Text Solution

    |