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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◦ logb (vw) = logb v + logb w◦ Example: log7 3 + log7 11 = log7 33
#2) Quotient Property◦ logb ( ) = logb v – logb w
◦ Example: log5 28 - log5 7 = log5 4
v
w
#3) Power Property◦ log (vk) = k log v◦ Example #1: log9 45 = 5 log9 4
◦ Example #2: log8 = log8 6½ = ½ log8 6
State the property used to rewrite each expression:◦ log3 32 – log3 8 = log3 4 quotient property
◦ log6 = log6 x power property
6
n pxp
n
YOUR TURNState the property used to rewrite each expression:◦ log5 2 + log5 6 = log5 12
◦ 3 logb 4 – 3 logb 2 = logb 8Product propertyPower & Quotient property
Write each logarithmic expression as a single logarithm◦ log3 20 – log3 4
◦ 3 log2 x + log2 y
= log3 20/4 Quotient Property= log3 5 Divide
= log2 x3 + log2 y Power Property
= log2 x3y Product Property
Your Turn Write 3 log 2 + log 4 – log 16 as a single
logarithm
log 2
Logarithms can also be expanded◦ log5 x/y
◦ log 3r4
◦ log2 7b
◦ log7 a3b4
log5 x - log5 y
log 3 + 4log r
log2 7 + log2 b
3log7 a + 4log7 b
Assignment◦ Page 457◦ 1 – 29, odd problems
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