Assignment

Write Remember Defi ne each term in your own words. The Product Rule of Logarithms states: “The 1. Zero Property of Logarithms logarithm of a product is equal to the sum of the 2. Logarithm with Same Base and Argument logarithms of the factors.” 3. Power Rule of Logarithms The Quotient Rule of Logarithms states: “The logarithm of a quotient is equal to the diff erence of the logarithms of the dividend and divisor.”

Practice 1. Use the properties of logarithms to rewrite each logarithmic expression in expanded form. ___x3 a. log (ab2c3) b. log 3 (5y2) ___2x c. log (6mn4) d. ln 2 (y10) 2. Use the properties of logarithms to rewrite each logarithmic expression as a single logarithm.

a. 2 log5 3 2 log5 y b. 7 ln x 1 ln 8 2 3 ln y c. 2(log 5 1 log m) 2 log (m3)

d. 8 log2 x 2 3(log2 y 1 2 log2 x)

3. Suppose loga 2 5 m, loga 5 5 n, and loga 7 5 t. Write an algebraic expression for each logarithmic expression.

a. loga 14 b. loga 20 ___5 ___1 c. log ( ) d. log ( ) a 14 a 49 ___10 e. loga 100 f. log ( ) a 7 ____I 5 4. An earthquake’s magnitude, M, can be determined using the formula M log ( 1024) , where I represents the intensity of the earthquake. Rewrite the logarithmic expression in the formula in expanded form. _____I 5 5. The loudness, L, of a sound, in decibels, can be determined using the formula L 10 log ( 10212) , © Carnegie Learning, Inc. where I represents the intensity of the sound. Rewrite the logarithmic expression in the formula in expanded form.

LESSON 2: Mad Props • M3-195

AA2_SE_M03_T03_L02.indd2_SE_M03_T03_L02.indd 195195 11/21/19/21/19 9:379:37 AMAM AA2_SE_M03_T03_L02.indd 196 2 _ S E _ M M3-196 • 0 3 _ 4. Determine the quadratic equation that goes through the points (1, points the ( 3), through goes that equation quadratic the Determine 4. 1. Solve for the unknown in each logarithmic equation. logarithmic ineach unknown the for 1.Solve Review log torewrite oflogarithms properties Use Stretch 2. Estimate log 2. Estimate 3. The Richter scale is used to rate the magnitude of an earthquake, or the amount of energy released. released. ofenergy amount the or ofanearthquake, magnitude the torate isused scale Richter 3. The T 0 3 taken 100 km from the epicenter of the earthquake), and and earthquake), ofthe epicenter the from 100 km taken (mea measured being earthquake ofthe intensity b. An earthquake in Mexico City measured 8.0 on the Richter scale. An earthquake was recorded in wasrecorded earthquake An scale. Richter the on 8.0 measured City inMexico earthquake An b. inChile anearthquake 7.9 measured while Francisco scale, inSan Richter the on earthquake An a. b. log a. log 10000 or “threshold quake” whose seismograph amplitude is10 amplitude seismograph whose quake” “threshold or d. log An earthquake’s magnitude, magnitude, earthquake’s An c. log _ L 0 2 Haiti that was three times stronger. wa times What wasthree that Haiti earthquake? Chilean wasthe intense more manytimes How 8.8. measured . i n d d __

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