Review of Logarithm for General Chemistry II Fall 2013 Dr. C. Yau

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.

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. 102 = 100, so x = 2 Thus, log 100 = 2 log 0.01 = -2 because 10 must be raised to power of -2 to give 0.01. (What is x if 10x = 0.01?) 10-2 = 0.01, so x = -2 Thus log 0.01 = -2

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 = 1.579783597 log 5.8x103 = 3.763427994 log 2.5 x 10-2 = - 1.602059991 log 6.2 x 10-4 = - 3.207608311

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 = 2.718281828.... 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.”

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 = 3.637586160 ln 5.8x103 = 8.665613197 ln 2.5 x 10-2 = -3.688879454 ln 6.2 x 10-4 = -7.385791080

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 = 0.0001

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 -2.87 = 10-2.87 = ? = 0.001348963 or 1.348963x10-3 antilog 8.78x10-3 = ? = 1.020422439 antilog 5.43x10-2 = ? = 1.133182868

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 0.782 = e0.782 = ? = 2.185839576 anti ln 4.28x10-2 = ? = 1.043729128

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

How will questions appear? log 2.5 x 10-3 = ? Ans. - 2.602059991 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. 660.6934480

Log x = 11.59 what is x? Ans. 3.90451x1011 ln x = - 0.49 what is x? Ans. 0.612626394 ln 1.07 = ? Ans. 0.067658648

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 = - 2.602059991 = - 2.60 ln 1.07 = 0.067658648 = 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. 660.6934480 = 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

Sig. fig. rules are confusing if you don’t practice using them! For more practice go to my tutorial: http://tinyurl.com/yegswku