Home
Class 11
MATHS
If (log)a3=2and (log)b8=3, then prove th...

If `(log)_a3=2`and` (log)_b8=3`, then prove that `(log)_a b=(log)_3 4.`

Text Solution

Verified by Experts

`log_a^3=2-(1)`
`log_b^8=3-(2)`
`(log_e^3/log_e^a)=2-(a)`
`(log_e^8/log_e^b)=3-(b)`
Dividing equation B from equation A
`(log_e^3*log_e^b)/(log_e^a*log_e^8)=2/3`
`(log_e^b)/(log_e^a)=2/3*(log_e^8/log_e^3)`
`log_a^b=2/3log_3^8`
...
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 log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4 .

If log_(a)3 = 2 and log_(b)8= 3 , then log_(a)(b) is-

Prove that (log_(2)8)/(log_(3)9) =3/2

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If (log)_a b=2,(log)_b c=2,a n d(log)_3c=3+(log)_3a , then the value of c//(a b) is............

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

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) a. A b. \ B c. \ C d. D

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))

Prove that log_3log_2log_(sqrt3) 81=1

Prove that log(1+2+3)=log1+log2+log3

CENGAGE ENGLISH-LOGARITHM-All Questions
  1. If (x(y+z-x))/(logx)=(y(z+x-y))/(logy) =(z(x+y-z))/(logz),p rov et h ...

    Text Solution

    |

  2. If (log)3y=xa n d(log)2z=x , find 72^x in terms of yand zdot

    Text Solution

    |

  3. If (log)a3=2and (log)b8=3, then prove that (log)a b=(log)3 4.

    Text Solution

    |

  4. Find the value of log tan1^0logtan2^0...........logtan89^0

    Text Solution

    |

  5. Sum of integers satisfying sqrt((log)2x-1)-1/2(log)2(x^3)+2>0 is......

    Text Solution

    |

  6. The value of b for which the equation 2(log)(1/(25))(bx+28)=-(log)5(12...

    Text Solution

    |

  7. The least integer greater than (log)2(15)* (log)(1/6)2 * (log)3 1/6 i...

    Text Solution

    |

  8. The reciprocal of 2/((log)4(2000)^6)+3/((log)5(2000)^6) is ..............

    Text Solution

    |

  9. The value of 5^((log)(1/5)(1/2))+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(lo...

    Text Solution

    |

  10. The value of N=((log)5 250)/((log)(50)5)-((log)5 10)/((log)(1250)5) is...

    Text Solution

    |

  11. If xa n dy are real numbers such that 2log(2y-3x)=logx+logy ,then fin...

    Text Solution

    |

  12. If loge((a+b)/2)=1/2(loge a+loge b), then find the relation between a ...

    Text Solution

    |

  13. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to

    Text Solution

    |

  14. The value of loga b-log|b|= loga (b) "log"|a| (c) -loga (d) none o...

    Text Solution

    |

  15. If (21. 4)^a=(0. 00214)^b=100 , then the value of 1/a-1/b is 0 (b) 1 ...

    Text Solution

    |

  16. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

    Text Solution

    |

  17. The number of N=6-(6(log)(10)2+(log)(10)31) lies between two successi...

    Text Solution

    |

  18. (log)4 18 is a rational number (b) an irrational number (c)a prime n...

    Text Solution

    |

  19. Solve: (log)((2x+3))(6x^2+23x+21)+(log)((3x+7))(4x^2+12 x+9)=4

    Text Solution

    |

  20. Given aa n db are positive numbers satisfying 4(log(10)a)^2+((log)2b)...

    Text Solution

    |