# Investigating Logarithms

Extracts from this document...

Introduction

Jeremiah Joseph

Investigating Logarithms

log2 + log3 | 0.7782 |

log6 | 0.7782 |

log3 + log7 | 1.322 |

log21 | 1.322 |

log4 + log 20 | 1.903 |

log80 | 1.903 |

log0.2 + log11 | 0.3424 |

log2.2 | 0.3424 |

log0.3 + log 0.4 | -0.9208 |

log0.12 | -0.9208 |

This table to the left clearly shows that the log of 2 numbers added together will equal the log of the number multiplied. The table below clearly shows that log (χ) + log (y) will equal log (χy). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can then be simplified to 10(a+b) =x*y. it is then possible to convert this back to log (xy) = a + b.

log5 + log4 | log20 | 1.301 |

log3 + log2 | log6 | 0.7782 |

log4 + log8 | log32 | 1.505 |

log6 + log3 | log18 | 1.255 |

log3 + log26 | log78 | 1.892 |

log7 + log4 | log28 | 1.447 |

log12 – log3 | 0.6021 |

log4 | 0.6021 |

log50 – log2 | 1.398 |

log25 | 1.398 |

log7 – log5 | 0.1461 |

log1.4 | 0.1461 |

log3 – log4 | -0.1249 |

log0.75 | -0.1249 |

log20 – log40 | -0.3010 |

log0.5 | -0.3010 |

Middle

log6 – log2 | log3 | 0.4771 |

log18 – log3 | log6 | 0.7782 |

log 16 – log 2 | log8 | 0.9031 |

log50 – log5 | log10 | 1 |

log25 – log5 | log5 | 0.6989 |

log32 – log8 | log4 | 0.6021 |

4 log2 | 1.204 |

log24 | 1.204 |

5 log6 | 3.891 |

log65 | 3.891 |

½ log4 | 0.3011 |

log41/2 | 0.3011 |

Conclusion

Let’s investigate the function y = log x

When x = 1, y = log1, therefore, y = 0

Therefore when y = 0, x will equal 1. On a graph this would mean that the curve would cut the x axis at 1. In this function x cannot equal zero or less than zero, this means that the restricted domain of the function will be {x: x>1}.

x | 0.000001 | 0.00001 | 0.0001 | 0.001 | 0.01 | 0.1 | 1 |

y = log x | -6 | -5 | -4 | -3 | -2 | -1 | 0 |

The table above displays that as x is multiplied by ten, the y value increases by 1.

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

y = log x | 0 | 0.3010 | 0.4771 | 0.6021 | 0.6989 | 0.7782 | 0.8451 | 0.9010 | 0.9542 | 1 |

The graph below demonstrates the curve of the function y = log x

Jeremiah Joseph Maths Internal Assessment Mr. Filander

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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