11 5 common logs and natural logs
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11-5 Common Logs and Natural Logs. 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. You can apply all properties to common logs. You can use a calculator to help. Evaluate:

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slide2

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
slide3

You can apply all properties to common logs. You can use a calculator to help.

  • Evaluate:
  • 1) log5(2)3 2) log
slide4

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

slide5

Use logarithms to solve

5) 63x = 81 6) 54z = 73

7) .25 = log16x

slide6

Sometimes, we can use our graphing calculators to help us solve logs

8) Solve by graphing 5x-1 = 2x

slide7

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)

slide8

Calculating Interest

Simple Interest Continuously Compounded

A= total, P = initial amount (principal)

r= rate n=times compounded t=time

slide9

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

slide10

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?

slide11

13) Convert log6 254 to a natural log, then evaluate.

14) Solve 6.5 = -16.25 lnx

15) Solve 48

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