Introduction to Logarithms

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Presentation transcript:

Introduction to Logarithms Lesson 7.4A Introduction to Logarithms

Solve 20 = 10x How can this be done? Can you estimate the answer to the nearest whole number? Can you use trial and error (with a calculator) to find the answer to the nearest tenth? There must be an easier way!

Logarithms are the inverses of exponents. They can “undo” them Logarithms are the inverses of exponents. They can “undo” them. And your calculator can do this for you (eventually)! Definition logba = c means bc = a

Rewrite in exponential form. a. log381 = 4 b. log10 100 = 2 c. log71 = 0

log x means log10x (common log) ln x means logex (natural log) 2. Rewrite in log form. a. 23=8 b. e0=1 c. 5-2 = 1/25 log x means log10x (common log) ln x means logex (natural log)

3. Evaluate without a calculator. log99 log 416 log28 log381 log71 ln e log 1000 log3 1 9

4. Evaluate with a calculator. Check mentally. a) log .01 b) ln e c) Can you find log49 with your calculator?

Back to 10x = 20 Rewrite this in log form. Can you use your calculator to solve the equation now?

Try solving these equations. 5. a) 10x – 5 = 432 b) 289 = 10x+7 c) 3ex = 150 d) 2ex+1 – 4 = 16

Last one How would you solve this equation? 3x+4 + 13 = 40 Or this one? 3x+4 + 13 = 45