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EXAMPLE 2

log. log. log. log. b. 0.2. a. 64. b. 5. 4. 4. To help you find the value of y , ask yourself what power of b gives you y. a. 4 to what power gives 64 ?. 4 3. 64 , so. 64. 3. =. =. b. 5 to what power gives 0.2 ?. 0.2 , so. 0.2. –1. 5 –1. log. =. =. 5.

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EXAMPLE 2

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  1. log log log log b. 0.2 a. 64 b 5 4 4 To help you find the value of y, ask yourself what power of bgives you y. a. 4 to what power gives 64? 43 64, so 64 3. = = b. 5 to what power gives 0.2? 0.2, so 0.2 –1. 5–1 log = = 5 EXAMPLE 2 Evaluate logarithms Evaluate the logarithm. SOLUTION

  2. log log log log log d. 125 c. 6 1/5 36 1/5 b 36 –3 1 1 To help you find the value of y, ask yourself what power of bgives you y. 5 5 c. to what power gives 125? 125, so 125 –3. = = 1 361/2 6, so 6 . d. 36 to what power gives 6? = = 2 EXAMPLE 2 Evaluate logarithms Evaluate the logarithm. SOLUTION

  3. log 8 a. 8 100.903 8 b. ln 0.3 .3 e –1.204 0.3 EXAMPLE 3 Evaluate common and natural logarithms Expression Keystrokes Display Check 0.903089987 –1.203972804

  4. Tornadoes The wind speed s(in miles per hour) near the center of a tornado can be modeled by s 93logd + 65 = where dis the distance (in miles) that the tornado travels. In 1925, a tornado traveled 220 miles through three states. Estimate the wind speed near the tornado’s center. EXAMPLE 4 Evaluate a logarithmic model

  5. s 93logd+ 65 = 93(2.342)+ 65 ANSWER The wind speed near the tornado’s center was about 283miles per hour. EXAMPLE 4 Evaluate a logarithmic model SOLUTION Write function. = 93log220+ 65 Substitute 220 for d. Use a calculator. = 282.806 Simplify.

  6. log log log log 5. 32 27 27 2 2 25 32, so 32 5. = = 6. 3 271/3 3, so 3 . 1 = = 3 for Examples 2, 3 and 4 GUIDED PRACTICE Evaluate the logarithm. Use a calculator if necessary. SOLUTION 2 to what power gives 32? SOLUTION 27 to what power gives 3?

  7. log 12 7. 12 101.079 12 8. ln 0.75 .75 e –0.288 0.75 for Examples 2, 3 and 4 GUIDED PRACTICE Evaluate the logarithm. Use a calculator if necessary. Expression Keystrokes Display Check 1.079 –0.288

  8. 9. WHAT IF?Use the function in Example 4 to estimate the wind speed near a tornado’s center if its path is 150miles long. s 93logd+ 65 = 93(2.1760)+ 65 ANSWER The wind speed near the tornado’s center is about 267 miles per hour. for Examples 2, 3 and 4 GUIDED PRACTICE SOLUTION Write function. = 93log150+ 65 Substitute 150 for d. Use a calculator. = 267 Simplify.

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