Use properties of logarithms to evaluate the. log

Transcription

1 EXAMPLE 1 Use properties of arithms 4 arithm. a. 4 7 Use and 47 = = to evaluate the Quotient property Use the given values of and b = 4 ( 7) Write 21 as 7. = = 2.19 Use the given values of and 4 47.

2 EXAMPLE 1 Use properties of arithms Use and 47 arithm. c. 449 = 47 2 = (1.404) = to evaluate the Write 49 as 7 2 Power property Use the given value of 47.

3 GUDED PRACTCE for Example 1 5 arithm Use and to evaluate the = = 0.2 Quotient property Use the given values of 5 and = (8 5) Write 40 as 8 5. = = Use the given values of 5 and 8.

4 GUDED PRACTCE for Example 1 Use and to evaluate the arithm = = 2 8 2(1.11) = 2.22 Write 4 as 8 2 Power property Use the given value of = = 5 (0.898) = 2.94 Write 125 as 5 Power property Use the given value of 5.

5 EXAMPLE 2 Expand a arithmic expression Expand 5x y 5x y = 5x y = 5 + x y = 5 + x y Quotient property Power property

6 EXAMPLE Standardized Test Practice = = (9 2 ) Power property = 9 2 = 24 Quotient property ANSWER The correct answer is D.

7 GUDED PRACTCE for Examples 2 and 5. Expand x 4. x 4 = + x 4 = + 4 x Power property

8 GUDED PRACTCE for Examples 2 and. Condense ln 4 + ln ln 12. ln 4 + ln ln 12 = ln 4 + ln ln 12 Power property = ln (4 ) ln 12 = ln 4 12 = ln 9 Quotient property

9 EXAMPLE 4 Use the change-of-base formula Evaluate 8 arithms. using common arithms and natural Using common arithms: 8 = Using natural arithms: 8 = ln ln

10 EXAMPLE 5 Use properties of arithms in real life Sound ntensity For a sound with intensity (in watts per square meter), the loudness L() of the sound (in decibels) is given by the function L() = 10 0 where 0 is the intensity of a barely audible sound (about watts per square meter). An artist in a recording studio turns up the volume of a track so that the sound s intensity doubles. By how many decibels does the loudness increase?

11 EXAMPLE 5 Use properties of arithms in real life Let be the original intensity, so that 2 is the doubled intensity. ncrease in loudness = L(2) L() = = = = Write an expression. Substitute. Distributive property Use a calculator. ANSWER The loudness increases by about decibels.

12 GUDED PRACTCE for Examples 4 and 5 Use the change-of-base formula to evaluate the arithm = =

13 GUDED PRACTCE for Examples 4 and 5 Use the change-of-base formula to evaluate the arithm = =

14 GUDED PRACTCE for Examples 4 and WHAT F? n Example 5, suppose the artist turns up the volume so that the sound s intensity triples. By how many decibels does the loudness increase? L() = 10 0 Let be the original intensity, so that is the tripled intensity.

15 GUDED PRACTCE for Examples 4 and 5 ncrease in loudness = L() L() = = = = Write an expression. Substitute. Distributive property Use a calculator. ANSWER The loudness increases by about decibels.