University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

103

Pages:

7
Author:

Houston Watkins

April-May Section 6-5: Properties of Logarithms (Part 2) 28-1 Target 6B We are learning the properties of logarithms so that we can solve logarithmic equations. The properties from last week will help us to evaluate logs that are not base 10 Product Property logb m + logb n logb mn Use 𝐥𝐨𝐠 𝟐 𝟑 logarithm. 1. log 2 21 𝟏. 𝟓𝟖𝟓 and 𝐥𝐨𝐠 𝟐 𝟕 2. log 2 𝟐. 𝟖𝟎𝟕 to evaluate each 3. log 2 49 Quotient Property logb m logb n logb m n Power Property log b m n n log b m To evaluate, we will use Use 𝒍𝒐𝒈𝟔 𝟓 the values given to us for logarithm. each set of problems. In addition to the ones that are given to use, we 4) 𝑙𝑜𝑔 can always use 𝒍𝒐𝒈𝒃 𝟏 𝟎. 𝟖𝟗𝟖 and 𝒍𝒐𝒈𝟔 𝟖 5) 𝑙𝑜𝑔 40 𝟏. 𝟏𝟔𝟏 to evaluate each 6) 𝑙𝑜𝑔 1 𝟎 This will work no matter what number you are given for the base 7) 𝑙𝑜𝑔 125 Summary: Today I learned This connects to what I know about What I learned today can help me later when 8) 𝑙𝑜𝑔 64 9) 𝑙𝑜𝑔 1 2 A2 4.28 – 5.1 Practice (Properties of logarithms Part 2) Use log 4 12 1.1 , log 4 7 0.8 and log 4 8 0.9 to evaluate each logarithm. 1. log 4 7 8 2. log 4 64 3. log 4 1 12 4. log 4 56 5. log 4 96 6. log 4 2 3 Algebra 2 Week 3 Assignment Use the properties of logarithms and the values below to find the logarithm indicated. Do not use a calculator to evaluate the logs. 1) log 3 8 ≈ 1.9 log 3 10 ≈ 2.1 log 3 11 ≈ 2.2 Find log 3 110 2) log 8 6 ≈ 0.9 log 8 11 ≈ 1.2 log 8 10 ≈ 1.1 Find log 8 121 3) log 6 4 ≈ 0.8 log 6 7 ≈ 1.1 log 6 10 ≈ 1.3 Find log 6 28 4) log 9 4 ≈ 0.6 log 9 11 ≈ 1.1 log 9 6 ≈ 0.8 11 Find log 9 4 5) log 7 9 ≈ 1.1 log 7 12 ≈ 1.3 log 7 10 ≈ 1.2 1 Find log 7 81 6) log 9 6 ≈ 0.8 log 9 4 ≈ 0.6 log 9 5 ≈ 0.7 1 Find log 9 5 7) log 9 5 ≈ 0.7 log 9 8 ≈ 0.9 log 9 6 ≈ 0.8 Find log 9 48 8) log 4 9 ≈ 1.6 log 4 6 ≈ 1.3 log 4 11 ≈ 1.7 Find log 4 121 -1- 9) log 3 10 ≈ 2.1 log 3 4 ≈ 1.3 log 3 7 ≈ 1.8 1 Find log 3 16 10) log 12 ≈ 1.1 log 8 ≈ 0.9 log 7 ≈ 0.8 Find log 64 11) log 7 ≈ 0.8 log 8 ≈ 0.9 log 12 ≈ 1.1 7 Find log 12 12) log 8 ≈ 0.9 log 7 ≈ 0.8 log 12 ≈ 1.1 Find log 144 Rewrite each logarithm using the "Power Property of Logarithms" 13) log 11 x 5 14) log 3 v x 16) log 2 a 9 18) log 8 6 x 15) log 6 13 17) log x 2 19) log 7 3 x 21) log 4 57 20) ln x x -2- 4 16 Solution Bank to Week 4 Assignment -0.3 𝑥 log 13 3.4 2.2 4 ln 𝑥 2 log 𝑥 -2.6 9 log 𝑎 2.4 𝑥 log 6 0.5 5 log11 𝑥 -0.7 4.3 1.9 1.8 1.7 𝑥 log 3 16 log 𝑣 𝑥 log 57 -2.2 Section 6-5: Properties of Logarithms (Part 2) April-May 28-1 Target 6B We are learning the properties of logarithms so that we can solve logarithmic equations. The properties from last week will help us to evaluate logs that are not base 10 Product Property Iogb m + Iogb n = Iog b mn Quotient Property m Iog b m - log b n = log b n Power Property log b m n = n Iog b m Use log2 3 = 1. 585 and log2 7 = 2. 807 to evaluate each logarithm. 1. log 2 21 \v32 ( 3"7) l0j2- '3 + IDJ:i. '1 L 58'5+ Ii. ,go7 � 4, � f �j l 3 2. log 2 -7 \032 3-1032- 7 1, 5g5 - 2. to7 ·I - L � :z l I _.,....__-- To evaluate, we will use Use log 5 = 0. 898 and log 8 = 1. 161 to evaluate each 6 6 the values given to us for logarithm. each set of problems. In addition to the ones that are given to use, we can always use This will work no matter what number you are given for the base Summary: Today I learned This connects to what I know about