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(a) Find a formula for the number of bacteria at time t. (b) Find the number of bacteria after one hour. (c) After how many minutes will there be 50 000 bacteria?
Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 7 log 22 2+ b) log 20 log 42 2− c) 3log 2 log 85 5+ d) 2log 8 5log 26 6− e) log 8 log 5 log 0.510 10 10+ − log 142, log 52, log 645, log 26, log 8010
Direction: Solve each logarithmic equations. Check your solutions to exclude extraneous answers. Show all your answer in the space provided.
Expand each logarithm. 1) ln (85 7) 4 20ln8 - 4ln7 2) ln (ca × b) lnc + lna 2 + lnb 2 3) ln (uv6) 5 5lnu + 30lnv 4) ln (x × y × z6) lnx + lny + 6lnz Condense each expression to a single logarithm. 5) 25ln5 - 5ln11 ln 525 115 6) 5lnx + 6lny ln (y6x5) 7) ln5 2 + ln6 2 + ln7 2 ln210 8) 20lna - 4lnb ln a20 b4 Use a calculator to approximate each ...
log . . . = logbX – logbY. logb(XY) = logbX + logbY Power Rule for Logarithms. Quotient Rule for Logarithms. Product Rule for Logarithms. The following examples show how to expand logarithmic expressions using each of the rules above.
•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
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