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# Module 25

### Common Logarithms, Natural Logarithms, and Change of Base

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

How do you find the common logarithm using a scientific calculator? | First, enter the number that is given in the question into the calculator. Then, locate and click on the "Log" key. For example, for log(59), you would type in '59', then press the Log key, and the display would show 1.77085201. Then round as suggested. |

Find the following answer, then round to 4 decimal places: log(12) | 1.0792 |

How do you find the natural logarithm using a scientific calculator? | First, enter the number that is given in the question into the calculator. Then, locate and click on the "LN" key. |

True or False: Loge 67 is the same thing as Ln67 | True. These are two different ways of expressing the same thing. |

Find the following answer, then round to 4 decimal places: Ln45 | Ln45 = 3.8067 |

Rewrite the following equation in exponential form. log x=3.1 | 10^3.1 = x Remember that a calculator is not necessary for this part. The base of the common log is understood to be 10, and by rewriting the equation this way, x can be isolated to one side and solved. |

Now that we have log x=3.1 converted to 10^3.1=x, please solve for x, and round to 4 decimal places. | x= 1258.9254 |

As a result of the property logb b^x=x we know Ln e^x=x. Therefore, find the exact value of: Ln e^-5 | -5. Ln e^-5= -5. Just as previously mentioned, a calculator is not necessary for this step. |

True or False: Is "e" just like "x" in that it can equal any number in an equation? | False. e is a predetermined number. It is the base of the natural logarithm, and its approximate value is 2.71828. If you are confused about this, think of it as something similar to the constant pi. e will always have the same value in any equation. |

Solve the equation for x. log x= 1.2 | x= 10^1.2 x=15.8489 Do not forget to first rewrite the equation using exponential form. |

What is the change of base formula? | logb a= ( logc a)/ (logc b) |

What is the purpose of the change of base formula? | Sometimes, a calculator is unable to obtain the value needed for a logarithm and needs to be rewritten in a way it can understand. |

Rewrite log 4 30 using the change of base formula. | (log 10 30)/(log 10 4) |