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Properties of Logarithms Date_____ Period____ Expand each logarithm. 1) log (6 ⋅ 11) log 6 + log 11 2) log (5 ⋅ 3) log 5 + log 3 3) log (6 11) 5 5log 6 − 5log 11 ... Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com. Title: Properties of Logarithms

Worksheet by Kuta Software LLC Algebra 2 Properties of Logarithms Name_____ ©G o2P0v1b7O \KYuptLaE xSEoDfztswqaGrLeT \LNLBCy.g W TAdlil` ZrBiXgqhHtYs\ GrCehsMe[rAvgeldx. Condense each expression to a single logarithm. 1) 4log 9 10 - 6log 9 3 log 9 104 36 2) 12log 7 10 - 2log 7 11 log 7 1012 112 3) 4log 9 7 + 24log 9 10 log 9 (1024 × 74) 4) 5log 2

PROPERTIES OF LOGARITHMS Definition: For 𝒚𝒚. x, b > 0, b. ≠. 1. 𝐥𝐥𝐥𝐥𝐥𝐥. 𝒃𝒃. 𝒙𝒙= 𝒚𝒚 𝒃𝒃= 𝒙𝒙. Natural Logarithm

Name: ___Math Worksheets _____ Date: _____ Created by: Effortless Math Education www.EffortlessMath.com 204 Properties of Logarithms Expand each logarithm. 1) (8×5 ...

WORKSHEET 7 Properties of Logarithms The following properties serve to expand or condense a logarithm or logarithmic expression so ... the properties of logarithms. log 2 0.3562, log 3 0.5646, log 5 0.8271 a a≈ ≈ ≈and a 21) 6 log a 5 22) log 18 a 23) log 100 a 24) log 30 a 25) log 3 a 26) log 75 a

Free 29 question Worksheet(pdf) with answer key on the properties of logarithms (product,quotient and power rules)

X + log b Y Product Rule for Logarithms The following examples show how to expand logarithmic expressions using each of the rules above. Example 1 Expand log 2 49 3 log 2 49 3 = 3 • log 2 49 Use the Power Rule for Logarithms. The answer is 3 • log 2 49 Example 2 Expand log 3 (7a) log 3 (7a) = log 3(7 • a) Since 7a is the product of 7 and ...

6.5 Properties of Logarithms – Summary on page 459 (see also page 426). Based on the fact that “logarithms are exponents” a nd thus follow the properties of exponents. Evaluate without a calculator: 1. ... worksheet 6.5 - 6.8 Author: spikek Created Date:

Use the properties of logarithms to write each logarithm in terms of a and/or b. Example: 3 2 2 ba 21. 6 22. 2 ln 3 23. ln8 (Hint: Use an exponent) 24. ln0.5 (Hint: Use a 1 – You know what ln 1 is) Use the Change-of-Base Formula, write it down, and a calculator to evaluate each logarithm. Round your answer to three decimal places. 25. 13 26 ...

Condense each expression to a single logarithm. 13) log 3 − log 8 14) log 6 3 15) 4log 3 − 4log 8 16) log 2 + log 11 + log 7 17) log 7 − 2log 12 18) 2log 7 3 19) 6log 3 u + 6log 3 v 20) ln x − 4ln y 21) log 4 u − 6log 4 v 22) log 3 u − 5log 3 v 23) 20log 6 u + 5log 6 v 24) 4log 3 u − 20log 3 v Critical thinking questions:

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 1) log 7 18 A) 2.1004 B) 0.4102 C) 1.4854 D) 0.6732 1) 2) log 12 53.9 A) 0.6524 B) 0.6232 C) 2.8108 D) 1.6045 2) Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate

©V OKLupteaf USToBf9tIwTaNrZeA xLfLYCI.A j BAlJlY 1rsi2g8h2tHsN 9r5erspeTrmvBeWdG.6 O 4MXaHdCeT 7woi2tWhO uIkn5fBiWnmi5toeU eAFlugDeJbJrVak G2m.4 Worksheet by Kuta Software LLC Voluntary Worksheet Logarithms: Expand, Condense, Properties, Equations Expand each logarithm. 1) ln (x6y3) 2) log 8 (x ⋅ y ⋅ z3) 3) log 9 (33 7) 4 4) log 7 (x3 y ...

Use the properties of logarithms and the values below to find the logarithm indicated. Do not use a calculator to evaluate the logs. 151) log 5 4 » 0.9 log 5 6 » 1.1 log 5 11 » 1.5 Find log 5 16 152) log 6 9 » 1.2 log 6 4 » 0.8 log 6 10 » 1.3 Find log 6 9 4 153) log 4 5 » 1.2 log 4 9 » 1.6 log 4 6 » 1.3 Find log 4 1 5 154) log 9 6 » 0 ...

24) log u log v log w log wvu Critical thinking questions: 25) (log x log y) (log log ) log x y 26) log x log Can't be simplified. Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com

Worksheet by Kuta Software LLC-2-11) log 5 c + log 5 a 3 + log 5 b 3 12) 5log 4 u − 6log 4 v 13) 3log 2 w + log 2 u 2 14) 3log 9 u + 9log 9 v 15) log 8 a + log 8 b + 3log 8 c 16) 20log 2 x − 4log 2 y Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the variables given. 17) log 8 7 = X log 8 ...

When dealing with logarithms, switching between exponential and Logarithmic form is often necessary. Logarithmic form Exponential Form log a bc abc Write each of the following in exponential form. 1) log 16 2 4 log 27 2) 9 1 log 3 2 3) 9 3 4) 4 1 log 2 16 Write each of the following in logarithmic form. 5) 3 814 6) 16 214 7) 36 12 1 6 8) 16 3254

Worksheet by Kuta Software LLC Honors Math 3 Properties of Logarithms ©s u2s0`1f7q EKNuwtgaG wSCoPfOtzwXakrneb HLNLUCr.p B yAnlOlb yrpiOgthFtysx frteHsreLrZvOeqdG. Expand each logarithm. 1) log 8 (x5 y) 2 2) log 9 (a b6) 6 3) log 9 (uv4) 3 4) log 2 (x × y × z4)

3.3 Logarithmic Properties Condense each expression to a single logarithm. 1) ... X G DMhaYd5eK 7wli OtHh u 0I Jnnf xiLn piMtYeW tA flFgbe nb6rDaW W2u.P Worksheet by Kuta Software LLC PreCalculus Name_____ Date_____ Hour____ ©o g2z0 E1 f3g HK Hujt CaK 5S GobfVtyw 1aMr6eq gLFLLC K. B 0 eA gl fl i XrxiKgmh FtzsS Tr9eHs Oenr evTeFdz. 8 ...

Rewrite each equation in logarithmic form. 1) 81 1 2 = 9 log 81 9 = 1 2 2) 142 = 196 log 14 196 = 2 Rewrite each equation in exponential form. 3) log x y = -18 x-18 = y 4) log y x = 12 y12 = x Use a calculator to approximate each to the nearest thousandth. 5) log 4 1.9 0.463 6) log 3 9 2 7) log 7 2.7 0.51 8) log 6 68 2.355 Expand each logarithm ...