Topic 2: Laws of Logarithms Logarithmic Functions

I can develop the laws of logarithms, using numeric examples and the exponent laws. I can determine an equivalent expression for a logarithmic expression by applying the laws of logarithms.

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You Should Notice… When adding logarithms of the same base, we can multiply the ‘insides’ of the logarithms. When subtracting logarithms of the same base, we can divide the ‘insides’ of the logarithms. Multiplying a constant by a logarithm is the same as raising the ‘inside’ to that same constant.

Information The logarithm laws are laws that can be used to simplify logarithmic expressions if all the terms have the same base. Since logarithms are exponents, the laws of logarithms are directly related to the exponent laws.

Information The laws of logarithms can be used to simplify logarithmic expressions if all the terms have the same base.

Example 1 Using one logarithmic law to evaluate logarithmic expressions a) b) c)

Example 2 Using multiple logarithmic laws to evaluate expressions a) b) c)

Example 3 Using logarithmic laws to express as a single logarithm Note: It’s a good idea to re-write this first… a) b) Remember:

Example 3 Using logarithmic laws to express as a single logarithm c) d) Move coefficients up into exponents. Simplify as necessary. Combine terms into a single logarithm.

Example 4 a) b) c) Using logarithmic laws to expand expressions Note: ln (pronounced ‘lawn’) means log base e. Note: log71 is equal to 0 since 7 to the power of 0 is 1.

Example 5 Express log8 in three different logarithmic forms. Expressing a logarithm in different logarithmic forms Express log8 in three different logarithmic forms. a) using a sum of logs b) using a difference of logs c) Using the product of an integer and a logarithm so…

Need to Know The logarithm laws are laws that can be used to simplify logarithmic expressions if all the terms have the same base. Since logarithms are exponents, the laws of logarithms are directly related to the exponent laws.

You’re ready! Try the homework from this section. Need to Know The laws of logarithms can be used to simplify logarithmic expressions if all the terms have the same base.