![]() And, logbb = 1 And, ln x = loge x We call it a Natural Log. Write down these hints: Remember: And, log 1 = 0 no matter what the base. DO NOT use your calculator until problem number 45. OR 3-6 All, 7-59 EOO for 5/5 pts Show Work. SOLUTION about decibelsĢ7 7.5 Assignment 7.5: 3-6 All, 7-59 ODD for 6/5 pts By how many decibels does the loudness increase? 11. 12 log 30 SOLUTION aboutĢ6 GUIDED PRACTICE for Examples 4 and 5 WHAT IF? In Example 5, suppose the artist turns up the volume so that the sound’s intensity triples. SOLUTION aboutĢ5 GUIDED PRACTICE for Examples 4 and 5 Use the change-of-base formula to evaluate the logarithm. ANSWER The loudness increases by about 3 decibels.Ģ4 GUIDED PRACTICE for Examples 4 and 5 Use the change-of-base formula to evaluate the logarithm. = 10 log – 2I I I Distributive property = 2 10 log I – + Product property 10 log 2 = Simplify. Increase in loudness = L(2I) – L(I) Write an expression. By how many decibels does the loudness increase? 10–12Ģ3 Use properties of logarithms in real lifeĮXAMPLE 5 Use properties of logarithms in real life SOLUTION Let I be the original intensity, so that 2I is the doubled intensity. An artist in a recording studio turns up the volume of a track so that the sound’s intensity doubles. SOLUTION Using common logarithms: = log 8 log 3 0.9031 0.4771 3 log 8 1.893 Using natural logarithms: = ln 8 ln 3 2.0794 1.0986 3 log 8 1.893Ģ2 EXAMPLE 5 Use properties of logarithms in real life Sound Intensity For a sound with intensity I (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function = log L(I) 10 I I where is the intensity of a barely audible sound (about watts per square meter). SOLUTION ln 9Ģ1 EXAMPLE 4 Use the change-of-base formula 3 log 8 Evaluate using common logarithms and natural logarithms. SOLUTION log log x Condense ln ln 3 – ln 12. ANSWERĢ0 GUIDED PRACTICE for Examples 2 and 3 Expand 5. 6 log 40 SOLUTION 2.059 SOLUTION 2.694ĮXAMPLE 2 Expand a logarithmic expression Expand 6 log 5x3 y SOLUTION 6 log 5x3 y = 5x3 y 6 log – Quotient property = 5 6 log x3 y – + Product property = 5 6 log x y – + 3 Power propertyĮXAMPLE 3 Standardized Test Practice SOLUTION – log 9 + 3log2 log 3 = – log 9 + log 23 log 3 Power property = log ( ) 23 – log 3 Product property = log 9 23 3 Quotient property = 24 log Simplify. 4 log = 2.808 Simplify.ġ7 GUIDED PRACTICE for Example 1 5 6 log Use 0.898 and 8 1.161 to evaluate the logarithm. 4 log 49 72 = 4 log Write 49 as 72 4 log = 2 7 Power property 2(1.404) Use the given value of 7. and = 2.196 Simplify.ĮXAMPLE 1 Use properties of logarithms 3 4 log Use 0.792 and 7 1.404 to evaluate the logarithm. ![]() 4 log 21 = 4 log (3 7) Write 21 as = 3 4 log + 7 Product property 0.792 1.404 + Use the given values of 3 4 log 7. 4 log 3 7 = 3 – 4 log 7 Quotient property 0.792 1.404 – Use the given values of 3 4 log 7. log8 4 ANSWERĮXAMPLE 1 Use properties of logarithms 3 4 log Use 0.792 and 7 1.404 to evaluate the logarithm. Try not to use a calculator except to guess and check. Properties of Logarithms Product Property Multiplication Addition Quotient Property Division Subtraction Power Property Exponent Multiplication AKA – The Bump The Bump Video – 1.5 min Bump Video – 1.5 min The Bump Music Video – 4 minġ4 cooldown Lesson 7.5, For use with pages 507-513Įvaluate the logarithm. Multiplication Addition Division Subtraction Exponent Multiplication ![]() ![]() Presentation on theme: "WARMUP Lesson 7.5, For use with pages Evaluate the logarithm."- Presentation transcript:ġ WARMUP Lesson 7.5, For use with pages 507-513 Evaluate the logarithm. ![]()
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