11-5 Common Logs and Natural Logs

1. 11-5 Common Logsand Natural Logs

2. Any log that has base 10 is called a common logarithm. We usually do not write the 10. • We can figure out many common logs easily • Ex) log 100 =2 • log 1000= 3

3. You can apply all properties to common logs. You can use a calculator to help. • Evaluate: • 1) log5(2)3 2) log

4. Sometimes, we can’t evaluate logs in our heads. Then, we use the change of base formula to help. Use change of base to evaluate: 3) Log91043 4) log8 172

5. Use logarithms to solve 5) 63x = 81 6) 54z = 73 7) .25 = log16x

6. Sometimes, we can use our graphing calculators to help us solve logs 8) Solve by graphing 5x-1 = 2x

7. e The number e is a famous irrational number, and is one of the most important numbers in mathematics. 2.7182818284590452353602874713527 (we will just use 2.718)

8. Calculating Interest Simple Interest Continuously Compounded A= total, P = initial amount (principal) r= rate n=times compounded t=time

9. Sometimes we use e in an exponential function. When we have base e, we use a natural logarithm (ln x) to solve. Solve 10) 18 = e 3x11) 4.5 > e .031x

10. In a study at White Oak, scientist found that time t=0, 5% of people have heard a rumor. After 2 days, 25% of students heard that rumor. How long will it take for 80% of White Oak Students to hear that rumor?

11. 13) Convert log6 254 to a natural log, then evaluate. 14) Solve 6.5 = -16.25 lnx 15) Solve 48