Logarithms Tutorial for Chemistry Students 1 Logarithms

Properties of Exponents and Logarithms

Therefore lnx = y if and only if ey = x. Most calculators can directly compute logs base 10 and the natural log. For any other base it is necessary to use
Exponents and Logarithms

Limits involving ln(x)

We can use the rules of logarithms given above to derive the following information about limits. lim x→∞ ln x = ∞ lim x→0.
. Limits Derivatives and Integrals

Significant Figure Rules for logs

Regular sig fig rules are guidelines and they don't always predict the correct The rule for natural logs (ln) is similar
Significant Figure Rules for logs

Logarithms

state and use the laws of logarithms. • solve simple equations requiring the use of logarithms. Contents. 1. Introduction log and ln.
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The laws of logarithms

a) 3 log10 5 b) 2 log x
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6.2 Properties of Logarithms

3. ln. ( 3 ex. )2. 4. log 3. √. 100x2 yz5. 5. log117(x2 − 4). Solution. 1. To expand log2. (8 x) we use the Quotient Rule identifying u = 8 and w = x and
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What is a logarithm? Log base 10

And so ln(ex) = x eln(x) = x. • Now we have a new set of rules to add to the others: Table 4. Functions of log base 10 and base e. Exponents. Log base 10.
logarithms

Logarithms Tutorial for Chemistry Students 1 Logarithms

There are four main algebraic rules used to manipulate logarithms: natural logarithms we can employ the following simple identity: ln(x)=2.303 log(x).
LogarithmsTutorial

Download Free Natural Logarithm Examples And Answers

5 days ago The 11 Natural Log Rules You Need to Know. Logarithm Questions and Answers ... Solving Natural Log Equations Solving a natural logarithmic.

Integration that leads to logarithm functions

ln x + c. In this unit we generalise this result and see how a wide variety of integrals result in logarithm functions. In order to master the techniques
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Boston University CH102 - General Chemistry Spring 2012

Logarithms Tutorial for Chemistry Students

1 Logarithms

1.1 What is a logarithm?

Logarithms are the mathematical function that is used to represent the number (y) to which a base integer (a) is

raised in order to get the numberx: x=ay; wherey= loga(x). Most of you are familiar with the standard base-10 logarithm: y= log10(x);

wherex= 10y. A logarithm for which the base is not specied (y= logx) is always considered to be a base-10

logarithm.

1.2 Easy Logarithms

The simplest logarithms to evaluate, which most of you will be able to determine by inspection, are those wherey

is an integer value. Take the power of 10's, for example:log

10(10) = 1 101= 10

log

10(100) = 2 102= 100

log

10(1000) = 3 103= 1000

log

10(10000) = 4 104= 10000

log

10(1) = 0 100= 1

log

10(0:1) =1 101= 0:1

log

10(0:01) =2 102= 0:01

log

10(0:001) =3 103= 0:001

log

10(0:0001) =4 104= 0:00011.3 Rules of Manipulating Logarithms

There are four main algebraic rules used to manipulate logarithms:

Rule 1:Product Rule

log auv= logau+ logav

Rule 2:Quotient Rule

log auv = logaulogav

Rule 3:Power Rule

log auv=vlogau 1 Boston University CH102 - General Chemistry Spring 2012

Caution!The most common errors come from students mistakenly using twocompletely ctitiousrules (there

are no rules that even resemble these): log a(u+v)6= logau+ logav(logarithm of a sum) and logb(uv)6= log bulogbv(logarithm of a dierence).

The practical implication of these rules, as we will see in the chapters dealing with thermodynamics, equilibrium,

and kinetics, is that we will be able to simplify complex algebraic expressions | easily.

1.4 Approximating Numerical Logarithms

In order to approximate the numerical values of non-trivial base-10 logarithms we will need (a) a good understanding

of the rules for manipulating logarithms and (b) the values of log2 and log3, which are 0:30 and 0:48, respectively.

Using these values and the rules we learned above, we can easily construct a table for the log values of integers

between 1 and 10:xlogxJustication1 0:00 By denition

2 0:30 Given

3 0:48 Given

4 0:60 log4 = log22= 2log2 = 2(0:3)

5 0:70 log10 = log25 = log2 + log5

6 0:78 log6 = log23 = log2 + log3

7 0:84 Estimated as 0:5(log6 + log8)

8 0:90 log8 = log23= 3log2 = 3(0:3)

9 0:96 log9 = log32= 2log3 = 2(0:48)

10 1:00 By denitionNotice that log7 was determined using the approximation that it is the half-way point between log6 and log8.

In general, as numbers become larger, the distance between their logarithms becomes smaller. Consequently, this

approach should work well for large numbers. A graphical representation of this table is:CH102-Exam 2SummerI,2009

Useful information

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100 cm, !E"mc

s #!T, 1 cal = 4.184 J. !E"!mc 2 , !E light "h', h"6.6%10 &34

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!mol,m e "9.1%10 &31 kg,J"kgm 2 !s 2 ,nm"10 &9 #m"10#!"1000#pm.

The table and figure below are of values of log

10 "x# versus x. Recall that ln"x#"2.303#log 10 "x#. xlog 10 "x#xlog 10 "x#

10.006 0.78

20.307 0.85

30.488 0.90

40.609 0.95

50.7010 1.00

Values of log

10 (x) for 1,x,10.

12345678910

x 0.30 0.48 0.60 0.70 0.78 0.85 0.90 0.95 Boston University CH102 - General Chemistry Spring 2012