Home
Class 12
MATHS
If (log)(10)5=aa n d(log)(10)3=b ,t h e ...

If `(log)_(10)5=aa n d(log)_(10)3=b ,t h e n` `(log)_(30)8=(3(1-a))/(b+1)` `(log)_(40)15=(a+b)/(3-2a)` `(log)_(243)32=(1-a)/b` (d) none of these

A

` log_(30) 8 = (3(1-a))/(b+1) `

B

` log_(40)15= (a+b)/(3-2a)`

C

` log_(243) 32 = (1-a)/b`

D

all of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(1) ` log_(30) 8 = (3log_(10)2)/(log_(10)5+log_(10) 3+log_(10)2)`
` = (3(1-log_(10)5))/(log_(10)5+log_(10)3+log_(10)2)`
` = (3(1-log_(10)5))/(1+log_(10)3) = (3(1-a))/(1+b)`
(2)` log_(40) 15=(log_(10)15)/(log_(10)40)`
` = (log_(10)3+log_(10)5)/(log_(10)5+3[1-log_(10)5])=(a+b)/(3-2a)`
(3) `log_(243)32 = (log_(10)2)/(log_(10)3)=(1-log_(10)5)/(log_(10)3) = (1-a)/b `
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Matrix Match Type|3 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Exercises (Single Correct Answer Type)|50 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

If (log)_(10)5=aa n d(log)_(10)3=b ,t h e n (A) (log)_(30)8=(3(1-a))/(b+1) (B) (log)_(40)15=(a+b)/(3-2a) (C) (log)_(243)32=(1-a)/b (d) none of these

If log_(30)3=a and log_(30)5=b find the value of log_(30)8

If log_(40)4 = a and log_(40)5 = b , then show that log_(40)16=4(1-a-b) .

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

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

If (log)_(10)[1/(2^x+x-1)]=x[(log)_(10)5-1] , then x= 4 (b) 3 (c) 2 (d) 1

If log_(a)b=10 and log_(6a)(32b)=5 find the value of a

If 1 + log_(10)a = 2log_(10)b , then express a in terms of b^2 .

If (log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6) in terms of a and b is equal to (a) (2a+3b-1)/(5a+b-2) (b) (5a+b-1)/(3a+2b-2) (c) (3a+b-2)/(2a+3b-1) (d) (2a+5b-2)/(3a+b-1)

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3- (log)_3 2 (c) log(3/2) (d) none of these

CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Multiple Correct Answers Type
  1. For a >0,!=1, the roots of the equation (log)(a x)a+(log)x a^2+(log)(a...

    Text Solution

    |

  2. The real solutions of the equation 2^(x+2). 5^(6-x)=10^(x^2) is/are 1 ...

    Text Solution

    |

  3. If (logx)/(b-c)=(logy)/(c-a)=(logz)/(a-b) , then which of the followin...

    Text Solution

    |

  4. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to

    Text Solution

    |

  5. If p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x), then

    Text Solution

    |

  6. Which of the following, when simplified, reduces to unity?

    Text Solution

    |

  7. If (log)a x=b for permissible values of aa n dx , then identify the st...

    Text Solution

    |

  8. The number of solutions of the equation log(x+1)(x-0.5)=log(x-0.5)(x+1...

    Text Solution

    |

  9. The equation sqrt(1+log(x) sqrt27) log(3) x+1 = 0 has

    Text Solution

    |

  10. If log(1//2)(4-x)gelog(1//2)2-log(1//2)(x-1),then x belongs to

    Text Solution

    |

  11. If the equation x^(log(a)x^(2))=(x^(k-2))/a^(k),a ne 0has exactly one ...

    Text Solution

    |

  12. The value of x satisfying abs(x-1)^(log3 x^2-2logx 9)=(x-1)^7 is

    Text Solution

    |

  13. If x = 9 is one of the solutions of log(e)(x^(2)+15a^(2))-log(e)(a...

    Text Solution

    |

  14. In which of the following, m gt n (m,n in R)?

    Text Solution

    |

  15. If (log)(10)5=aa n d(log)(10)3=b ,t h e n (log)(30)8=(3(1-a))/(b+1) ...

    Text Solution

    |

  16. The value of (6 a^(log(e)b)(log(a^(2))b)(log(b^(2))a))/(e^(log(e)a*lo...

    Text Solution

    |

  17. The inequality sqrt(x^((log)2sqrt(x)))geq2 is satisfied (a) by only on...

    Text Solution

    |

  18. If 3^(x) = 4^(x-1) , then x =

    Text Solution

    |