8d - Properties of Logarithms

Product Property Here is the product property: Using this form, expand the following: In order to simplify, use the product property and separate the 3 and the x. Whenever you see a problem that is multiplied together, separate it and change the sign to addition.

Division Property Here is the division property: Using this form, expand the following: Use the division property to separate the 3 and the x. Whenever you see a logarithm that has division in it, you must change that to subtraction if you want to expand it.

Exponent Property Here is the exponent property: Using this form, expand the following: First, use the product property to separate the x and y into an addition problem. Next, use the exponent property to put the exponent in front of the log. For example, since “3” is the exponent of “x”, the “3”will be placed in the front of the logarithm.

Multiple Properties (more challenging) First separate the fraction by subtracting the denominator form the numerator using the division property Second, split what is being subtracted into two by adding the 3 and the y while placing the y's power of two in front of its log by using the product property ***Remember to place parenthesis around the logs that are being added together because they were pulled form the denominator as a whole at the beginning*** Expand:

Multiple Properties (con’t) Condense: First using the exponent property place any numbers in front of logs into their position as an exponent Then, using order of operations and product property, multiply 4 and x to the third power together and then use the division property to make logx a denominator as just x Lastly notice the subtraction sign in front of log6, indicating the division property should be used again placing 6 in the denominator with x