Review of Logarithmfor General Chemistry II

Spring 2014Dr. C. Yau

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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.

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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 = 2Thus, log 100 = 2log 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 = -2Thus log 0.01 = -2

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Log of a Number on the CalculatorFind 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 = 1.579783597log 5.8x103 = 3.763427994log 2.5 x 10-2 = - 1.602059991log 6.2 x 10-4 = - 3.207608311

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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.”

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

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AntilogAntilog 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 = 0.00017

Anti-log of a Number on the CalculatorThe 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 = ? = 1.020422439antilog 5.43x10-2 = ? = 1.133182868 8

Anti-ln of a number on the CalculatorAnti-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 = ? = 2.185839576anti ln 4.28x10-2 = ? = 1.043729128

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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) = APractice by proving the following: log A/B = - log B/A

Note:log (A + B) log A + log B

How will questions appear?

log 2.5 x 10-3 = ? Ans. - 2.602059991log 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 LogarithmWhen 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 answere.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