Home
Class 12
MATHS
The value of (log(10)2)^(3)+log(10)8 * l...

The value of `(log_(10)2)^(3)+log_(10)8 * log_(10) 5 + (log_(10)5)^(3)` is _______.

Text Solution

Verified by Experts

The correct Answer is:
1
Let ` log_(10)2 = p and log_(10) 5 = q`
Hence, p+q = 1
` x = p^(3) + 3pq + q^(3)`
` = (p+q)^(3) - 3 pq(p+q)+3 pq`
` = 1-3pq+3pq`
= 1
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise JEE Previous Year|5 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The value of (log_(10)2)^(3)+log_(10)8log_(10)5+(log_(10)5)^(3) is

The value of 6^(log_(10)40)*5^(log_(10)36) is

The value of (1)/(5) log_(10) 3125 -4 log_(10)2 +log_(10)32 is

The value of (log_(3)8)/(log_(9)16log_(4)10)

The value of sqrt((log_(16)10)/(log_(2)10)+(log_(81)10)/(log_(27)10)), is

What is the value of (1/3 log_(10)125 - 2log_(10)4 + log_(10)32 + log_(10)I) ?

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

log_(10)3+log_(10)2-2log_(10)5

Find the value of log_(10)5*log_(10)20+(log_(10)2)^(2)

The value of log_(10)1 + log_(10) 10 + log_(10)100+ …….. log_(10)(10000000000)

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Numerical)
  1. If log(a)b=2, log(b)c=2, and log(3) c= 3 + log(3) a,then the value of...

    Text Solution

    |

  2. The value of (log(10)2)^(3)+log(10)8 * log(10) 5 + (log(10)5)^(3) is .

    Text Solution

    |

  3. If log(4)A=log(6)B=log(9)(A+B)," then "[4(B//A)]("where "[*] represent...

    Text Solution

    |

  4. Integral value of x which satisfies the equation =log6 54+(log)x 16=(l...

    Text Solution

    |

  5. If a = log(245) 175 and b = log(1715) 875, then the value of (1-ab)/...

    Text Solution

    |

  6. The difference of roots of the equation (log(27)x^(3))^(2) = log(270x^...

    Text Solution

    |

  7. Sum of integral values of x satisfying the inequality 3^((5/2)log3(12-...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Sum of integers satisfying sqrt(log(2)x-1)-1//2 log(2)(x^(3))+2 gt 0 ...

    Text Solution

    |

  11. Number of integers satisfying the inequality log(1//2)|x-3| gt -1 i...

    Text Solution

    |

  12. Number of integers le 10 satisfying the inequality 2 log(1//2) (x-1)...

    Text Solution

    |

  13. The value of (sqrt(3+2sqrt2)+sqrt(3-2sqrt2))^(2^(9)) is .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. if x+log10 (1+2^x)=xlog10 5+log10 6 then x

    Text Solution

    |

  17. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

    Text Solution

    |

  18. If a=log(12)18 and b=log(24)54 then find the value of ab+5(a-b)

    Text Solution

    |