Home
Class 12
MATHS
Solve the system of equations: (log)a x(...

Solve the system of equations: `(log)_a x(log)_a(x y z)=48(log)_a y log_a(x y z)=12 ,\ a >0,\ a!=1(log)_a z log_a(x y z)=84\ `

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Solve the system of equations log_2y=log_4(xy-2),log_9x^2+log_3(x-y)=1 .

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

x^((log_x)log_a ylog_y z) is equal to

x^((log_x)log_a ylog_y z) is equal to

Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) = 3 ^(log y) .

Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) = 3 ^(log y) .

Solve the equations log_1000 |x+y| = 1/2 . log_10 y - log_10 |x| = log_100 4 for x and y

Solve the differential equation x(dy)/(dx)=y(log y - log x +1) .

For positive numbers x ,\ y\ a n d\ z the numerical value of the determinant |1(log)_x y(log)_x z(log)_y x1(log)_y z(log)_z x(log)_z y1| is- a. 0 b. logx y z c. "log"(x+y+z) d. logx\ logy\ logz

Find the real solutions to the system of equations log_(10)(2000xy)-log_(10)x.log_(10)y=4 , log_(10)(2yz)-log_(10)ylog_(10)z=1 and log_(10)zx-log_(10)zlog_(10)x=0

ALLEN-LOGARITHMS-All Questions
  1. Find the value of 49^A+5^B w h e r e\ A=1-(log)7 2\ &\ B=-(log)5 4.

    Text Solution

    |

  2. If 4^A+9^B=10^C ,\ where A=(log)(16)4,\ B=(log)3 9\ &\ C=(log)x 83 th...

    Text Solution

    |

  3. Solve the system of equations: (log)a x(log)a(x y z)=48(log)a y loga(x...

    Text Solution

    |

  4. The vlaue of (81^((1)/(log(5)9))+3^((3)/(log(sqrt(6))3)))/(409)((sqrt(...

    Text Solution

    |

  5. Compute the following 56+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)(1//2)...

    Text Solution

    |

  6. The value of 4^(5log(4sqrt(2)(3-sqrt(6))-6log(8)(sqrt(3)-sqrt(2)))) is

    Text Solution

    |

  7. (1/2)^logx^2+2> 3.2^(-"log"(-x))

    Text Solution

    |

  8. Solve (log)x2(log)(2x)2=(log)(4x)2.

    Text Solution

    |

  9. Solve for x :(log)("x"+1)(x^2+x-6)^2=4

    Text Solution

    |

  10. The number of positive integers satisfying x+(log)(10)(2^x+1)=x(log)(1...

    Text Solution

    |

  11. If a^(2) + b^(2) -c^(2) = 0, " then" (1)/("log"(c+a)b) + (1)/("log"(c-...

    Text Solution

    |

  12. Given (log)(10)34. 56=1. 5386 ,\ find (log)(10)3. 456 ;(log)(10)0. 34...

    Text Solution

    |

  13. Find the number of positive integers which have the characterstics 3, ...

    Text Solution

    |

  14. If (log)(10)2=0. 3010\ &(log)(10)3=0. 4771.\ Find the value of (log...

    Text Solution

    |

  15. Find the antilogarihtm of 0.75 if the base of the logarithm is2401

    Text Solution

    |

  16. If x ,\ y >0,(log)y x+(log)x y=(10)/3\ a n d\ x y=144 ,\ t h e n(x+y...

    Text Solution

    |

  17. let y=sqrt(log2(3)log2(12)log2(48)log2(192)+16)-log2(12)log2(48)+10fin...

    Text Solution

    |

  18. If x=1+(log)a b c ,\ y=1+(log)b c a\ a n d\ z=1+(log)c a b ,\ then pr...

    Text Solution

    |

  19. A rational number which is 50 times its own logarithm to the base 10 ...

    Text Solution

    |

  20. The value of a^(sqrt((log)a b))-b^(sqrt((log)b a))(w h e r ea ,b >0a n...

    Text Solution

    |