PROPERTIES OF LOGARITHMS



Properties of Logarithms |Example: |Expand to more than one logarithm |Condense to only one logarithm | |

|Product Property of Logarithms | | | |

|[pic] | |log xyz = _______________ |log 2 + log x + log y = |

| |log 5x = ________________ | | |

|Think: | | |____________________ |

|(xm)(xn) = x(m + n) | | | |

| |_____________ = log 4 + log y | | |

|Division Property of Logarithms |Example: | | |

| | |log [pic]= __________________ |log 2 – log y = ____________ |

|[pic] | | | |

|Think: |log [pic] = _____________ | | |

|xm = x(m – n) | | | |

|xn |____________ = log 7 – log x | | |

|Power Property of Logarithms | | | |

| | | | |

|[pic] |log b x3 = ________________ |log x2 = ______________ |3 log y = _______________ |

|Think: | | | |

| | |log [pic]= _____________ |x log 5 = _______________ |

|(xn)m = xnm |__________ = ½ log b x | | |

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