Essential Question: What are the three properties that simplify logarithmic expressions? Describe how to use them.

 Rule: All logs must share the same base in order to be expanded/compressed  #1) Product Property ◦ log b (vw) = log b v + log b w ◦ Example: log log 7 11 = log 7 33  #2) Quotient Property ◦ log b ( ) = log b v – log b w ◦ Example: log log 5 7 = log 5 4

 #3) Power Property ◦ log (v k ) = k log v ◦ Example #1: log = 5 log 9 4 ◦ Example #2: log 8 = log 8 6 ½ = ½ log 8 6  State the property used to rewrite each expression: ◦ log 3 32 – log 3 8 = log 3 4quotient property ◦ log 6 = log 6 xpower property

 Y OUR T URN State the property used to rewrite each expression: ◦ log log 5 6 = log 5 12 ◦ 3 log b 4 – 3 log b 2 = log b 8 Product property Power & Quotient property

 Write each logarithmic expression as a single logarithm ◦ log 3 20 – log 3 4 ◦ 3 log 2 x + log 2 y = log 3 20 / 4 Quotient Property = log 3 5Divide = log 2 x 3 + log 2 yPower Property = log 2 x 3 yProduct Property

 Your Turn  Write 3 log 2 + log 4 – log 16 as a single logarithm log 2

 Logarithms can also be expanded ◦ log 5 x / y ◦ log 3r 4 ◦ log 2 7b ◦ log 7 a 3 b 4 log 5 x - log 5 y log 3 + 4log r log log 2 b 3log 7 a + 4log 7 b

 Assignment ◦ Page 457 ◦ 1 – 29, odd problems