# Logarithm

## Logarithm

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Question 1 |

If log 27 = 1.431, then the value of log 9 is:

0.934 | |

0.945 | |

0.954 | |

0.958 |

Question 1 Explanation:

log 27 = 1.431
=>log (3(^3 ) = 1.431
==>3 log 3 = 1.431
==>log 3 = 0.477
==>log 9 = log(3^2) = 2 log 3 = (2 x 0.477) = 0.954.

Question 2 |

If log(a/b)+log(b/a)= log (a + b), then:

a + b = 1 | |

a - b = 1 | |

a = b | |

a^2 - b^2 = 1 |

Question 2 Explanation:

log (a + b) = log((a/b)*(b/a)) ==> log 1.
So, a + b = 1.

Question 3 |

If log 2 = 0.30103, the number of digits in 2^64 is:

18 | |

19 | |

20 | |

21 |

Question 3 Explanation:

log (2^64)= 64 x log 2
= (64 x 0.30103)
= 19.26592
Its characteristic is 19.
Hence, then number of digits in 264 is 20.

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