Chapter 9 Resource Masters - …

1 Chapter 9A7 Glencoe Algebra 2 AnswersCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, (Lesson 9-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, _____ DATE_____ PERIOD _____Chapter 917 Glencoe Algebra 2 Lesson 9-2 Write each equation in logarithmic 125log5125 1log71 81log381 4 5. 3 15 6log3 4log 14 3log77766 Write each equation in exponential 363 626 43 4 10 5 12 532 35 8 Evaluate each 13 27 (n 1)n each equation or inequality. Check your 3x 15 x 00 q (2y 8) 2y (3x 7) log8(7x 4) (8x 20) log7(x 6) (x2 2) log3xx equation for loudness, in decibels, is L 10 log10R, where Ris the relativeintensity of the sound.

2 Sounds that reach levels of 120 decibels or more are painful tohumans. What is the relative intensity of 120 decibels? invests $1000 in a savings account that pays 4% interestcompounded annually. The value of the account Aat the end of five years can bedetermined from the equation log A log[1000(1 )5]. Find the value of Ato thenearest dollar.$12173 41 81 23 21 10001 2561 31 492 31 163 51 21 811 811 51 641 811 641 41 81 PracticeLogarithms and Logarithmic FunctionsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 916 Glencoe Algebra 2 Write each equation in logarithmic 8log28 9log39 2 log8 24. 2 log 13 2 Write each equation in exponential 535 343 9 12 25 2 Evaluate each Solve each equation or inequality.

3 Check your 00 y 14 x 2n (4x 12) (4x 4) 5x (x 2) log3(3x) (3y 5) log6(2y 3)y 81 21 41 641 31 31 6251 641 31 21 251 251 21 91 91 31 641 64 NAME _____ DATE_____ PERIOD _____9-29-2 Skills PracticeLogarithms and Logarithmic FunctionsChapter 9A10 Glencoe Algebra 2 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, (Lesson 9-3)Skills PracticeProperties of Logarithms9-3 NAME _____ DATE_____ PERIOD _____Chapter 923 Glencoe Algebra 2 Lesson 9-3 Use log23 and log25 to approximate the value of each equation. Check your 3 log74 2 log4x log68 log58 log23 2 log95 log82 log84 log10(3x 5) log4(2x 3) log33 log10(2 y) 2 log25 (x 4) log2(x 3) (n 1) log4(n 2)

4 Log512 3 log52 log5a151 259 51 35 33 5 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 922 Glencoe Algebra 2 Solve Logarithmic EquationsYou can use the properties of logarithms to solveequations involving each 2 log3x log34 log3252 log3x log34 log325 Original equationlog3x2 log34 log325 Power Propertylog3 log325 Quotient Property 25 Property of Equality for Logarithmic Functionsx2 100 Multiply each side by 10 Take the square root of each logarithms are undefined for x 0, 10 is an extraneous only solution is log2x log2(x 2) 3log2x log2(x 2) 3 Original equationlog2x(x 2) 3 Product Propertyx(x 2) 23 Definition of logarithmx2 2x 8 Distributive Propertyx2 2x 8 0 Subtract 8 from each side.

5 (x 4)(x 2) 2orx 4 Zero Product PropertySince logarithms are undefined for x 0, 4 is an extraneous only solution is each equation. Check your log52x log46 log48 log6x log2(x 3) log28 log63 log6(x 1) log4(x 1) log4(11 x) 3 log25 2 log21012, log2x 2 log25x (c 3) log3(4c 1) (x 3) log5(2x 1) 24 78 195 21 2x2 4x2 4 Study Guide and Intervention (continued)Properties of LogarithmsNAME _____ DATE_____ PERIOD _____Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 9A11 Glencoe Algebra 2 AnswersCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, (Lesson 9-3)9-3 Word Problem PracticeProperties of LogarithmsNAME _____ DATE_____ PERIOD _____Chapter 925 Glencoe Algebra 2 Lesson 9-3 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, COMPUTATIONJ essica hasmemorized log52 and log53 Using this information, to thenearest thousandth, what power of 5 isequal to 6?

6 Chemist is formulating anacid. The pH of a solution is given by log10C,where C is the concentration ofhydrogen ions. If the concentration ofhydrogen ions is increased by a factor of 100, what happens to the pH of thesolution?The pH decreases by MATHF rank is solving aproblem involving logarithms. He doeseverything correctly except for one mistakenly writeslog2a log2b log2(a b).However, after substituting the valuesfor aand bin his problem, he amazinglystill gets the right answer! The value of awas 11. What must the value of bhave been? has two poles. Onepole has length equal to log721 and the other has length equal to the length of both poles joinedend to end as the logarithm of a Exercises 5-7, use thefollowing wanted to try to quantify the termspuny, tiny, small, medium, large, big, huge,and picked a number of objects and classified them with theseadjectives of size.

7 She noticed that the scaleseemed exponential. Therefore, she came upwith the following definition. Define Sto be log3V, where Vis volume in cubic use the following table to find theappropriate an expression for Sapplied to a cube in terms of where is the sidelength of a many cubes, each one foot on a side, would have to be put together to get an object that Alicia would call big ? likely is it that a large objectattached to a big object would result in a huge object, according to Alicia s very likely; most likely theresult will be big, not 2 S 1tiny 1 S 0small0 S 1medium1 S 2large2 S 3big3 S 4huge1 3 PracticeProperties of Logarithms9-3 Chapter 924 Glencoe Algebra 2 Use log105 and log107 to approximate the value of each equation.

8 Check your log69 log8w (3u 14) log95 log2x log25 log316 5 log22 (3m 5) log10m (b 3) log10b (t 10) log8(t 1) (a 3) log3(a 2) (r 4) log10r log10(r 1) (x2 4) log4(x 2) log10w (n 3) log8(n 4) log5(x2 9) 6 0 (9x 5) log16(x2 1) (2x 5) 1 log6(7x 10) (5y 2) 1 log2(1 2y) (c2 1) 2 log10(c 1) 2 log7x log73 that the loudness Lof a sound in decibels is given by L 10 log10R,where Ris the sound s relative intensity. If the intensity of a certain sound is tripled, byhow many decibels does the sound increase?about earthquake rated at on the Richter scale is felt by many people,and an earthquake rated at may cause local damage. The Richter scale magnitudereading mis given by m log10x, where xrepresents the amplitude of the seismic wavecausing ground motion.

9 How many times greater is the amplitude of an earthquake thatmeasures on the Richter scale than one that measures times1 21 41 33 22 325 75 77 5 NAME _____ DATE_____ PERIOD _____Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies.