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# Module 24

### Logarithmic Functions and Properties of Logarithms

Question | Answer |
---|---|

Definition of a logarithm | If b>0 and b does not equal one, then y=log base b of x means x=b ^y for every x>0 and every real number y. |

Characteristics of Logarithmic Functions | f(x)=log base b of x, b>o, b doesn't =1. It is a one-to-one function, x-intercept (1,0), no y-intercept, the domain is from zero to infinity, and the range is from negative infinity to infinity. |

Form for a logarithmic expression | Log(sub b)x=y |

Graphing of logarithmic functions | In order to graph all must do is plug in the x values greater then zero into your calculator. Your graph will always pass through (1,0). |

Write the difference as the logarithmic function of a single number: log_7 (12) - log_7 (4) | Step1: Use the definition of Quotient Property of logarithm: log_b (x/y)= log_b (x) - log_b (y). Step2: Identify the values that correspond to x,y,b: x= 12, y=4, b=7. Step3: Find the difference: log_7 (12) - log_7 (4) = log_7 (12/4)= log_4 (3) |

Logarithm rules | 1) logb(mn) = logb(m) + logb(n) 2) logb(m/n) = logb(m) – logb(n) 3) logb(mn) = n · logb(m) |