1. Review of Logarithm for General Chemistry II
Fall 2014
Dr. C. Yau

2. Introduction
This is meant to be just a review of logarithm. We will discuss ONLY what you need to know about logarithm in this course. For a full discussion of logarithm, please refer to a math textbook or see a math tutor.

3. What is meant by “log”?
“Log” means log based 10 (or log10). To find the log of a number means to find the exponent to which 10 must be raised to give that number. log 100 = ? This is asking what is x if 10x = 100. log 100 =2 because 10 must be raised to power of 2 to give = 100, so x = 2 Thus, log 100 = 2 log 0.01 = -2 because 10 must be raised to power of -2 to give (What is x if 10x = 0.01?) 10-2 = 0.01, so x = -2 Thus log 0.01 = -2

4. Log of a Number on the Calculator
Find the “LOG” key on your calculator and make sure you are getting the right answer.
For now, don’t worry about sig. fig. They follow very different rules that you have learned so far and will be explained later.
Are you getting the correct ans from your calculator?
log 38 =
log 5.8x103 =
log 2.5 x 10-2 =
log 6.2 x 10-4 =

5. What is meant by “ln”?
“Ln” means log based e (or loge). In this class we will refer to ln and not loge. What is e? e = Don’t ask me why! That is beyond the scope of those course. Get an explanation from your math professor. We refer to ln as the “natural log.”

6. Ln of a Number on the Calculator
Find the “LN” key on your calculator, usually located near the “LOG” key. Check to see that you are getting right answers: ln 38 = ln 5.8x103 = ln 2.5 x 10-2 = ln 6.2 x 10-4 =

7. Antilog
Antilog is also referred to as the inverse log. Recall that... the log of a number means to find the exponent to which 10 must be raised to give that number. Antilog means the reverse operation of log. Antilog of a number means to find the number when 10 is raised to the power of that number. (What is 10x when given x?) e.g. antilog 3 means what is 103 ? antilog 3 = 103 = 1000 antilog -4 means what is 10-4 ? antilog -4 = 10-4 =

8. Anti-log of a Number on the Calculator
The antilog (or inverse log) key on your calculator is usually the SAME key as your LOG key except you would need to press the 2nd function key. It is usually marked as 10x. antilog = = ? = or x10-3 antilog 8.78x10-3 = ? = antilog 5.43x10-2 = ? =

9. Anti-ln of a number on the Calculator
Anti-ln is also referred to as the inverse natural log. The key for anti-ln is usually the SAME key as your LN key except you would need to press the 2nd function key. It is usually marked as ex. anti-ln = e0.782 = ? = anti ln 4.28x10-2 = ? =

10. Properties of Logarithm
Know these well:
log AB = log A + log B
log A/B = log A – log B
log AB = B log A
log A/B = - log B/A
antilog (log A) = A
Practice by proving the following:
Note:
log (A + B)  log A + log B

11. How will questions appear?
log 2.5 x 10-3 = ?
Ans
log x = 2.82, what is x?
To solve this, find the antilog of both sides:
Antilog log x = antilog 2.82
x = antilog 2.82 = ?
Ans

12. Log x = what is x?
Ans x1011
ln x = what is x?
Ans
ln 1.07 = ?
Ans

13. Sig. Fig. Rules for Logarithm
When calculating log of a number,
# sig.fig. of that number
= # decimal places of the answer
e.g. log 2.5 x 10-3 = =
ln 1.07 = = 0.068
When calculating the inverse log of a number,
# decimal places = # sig. fig. of the answer
e.g. log x = 2.82, what is x?
Ans = 6.6x102
log x = 1.54x10-1, what is x?
Watch out! This is tricky!
Ans. 1.43
Why is it not 1.4?
3 sig. fig.
3 decimal places

14. Sig. fig. rules are confusing if you don’t practice using them!
For more practice go to my tutorial: