1. Introduction to Logarithms
Lesson 7.4A
Introduction to Logarithms

2. 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!

3. 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

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

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

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

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

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

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

10. Last one
How would you solve this equation? 3x = 40 Or this one? 3x = 45