Download presentation

1
Logarithms ISP 121

2
What is a Logarithm? A logarithm (or log) is a number that represents a power or exponent Why use logs? A simpler way to express large values Some things grow or shrink exponentially, so the log is a perfect “numbering” system

3
**What is a Logarithm? Logarithms are exponents in disguise.**

The output of a logarithm is an exponent log b X = Y ↔ bY = X The first equation is in “log form” and the second equation is in “exponent form”

4
**Converting and Solving**

log3 27 = y 3y = 27 y = 3 So log3 27 = 3 log7 49 = y 7y = 49 y = 2 So log7 49 = 2 log525 = y 5y = 25 Y = 2 log525 = 2 log5125 = y 5y = 125 Y = 3 log5125 = 3

5
Log Base 10 The log base 10 (written log10 or just log) is a very common log log10 x is the power to which 10 must be raised to obtain x Or better yet, 10 to what power equals x?

6
Log Base 10 Solve the following without a calculator: log = y 10y = 100 102 = 100 log = 2 Log = y 10y = 1000 103 = 1000 log = 3 log10 10,000 = y 104 = 10,000 log10 10,000 = 4 Log10 10,000,000 = y 107 = 10,000,000 log10 10,000,000 = 7

7
**Log Base 10 Review the answers.**

Solve the following with a calculator: Review the answers. With log base 10, how do the answers change when x is multiplied by 10? y increases by 1 For log base 10, when y increases by 1, x is multiplied by 10 log10 3 = y log10 3 = .4771 Log10 30 = y log10 30 = Log = y log =

8
**Log Base 10 log 2.5 = y Log 2.5 = .39794 So what is log 25? Log 250?**

Use what we learned in the last slide. Remember, log = log10 log 2.5 = y Log 2.5 = So what is log 25? Log 250? Log 25000? log 25 = log 250 = log 2500 = Log x = 1 101 = 10 X = 10 So what is x if log x = 2? what is x if log x = 3? what is x if log x = 4? what is x if log x = 6? log x = 2 x = 100 log x = 3 x = 1000 log x = 6 x = 100,000

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google