• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16
17. 17
17
18. 18
18

# The reasoning behind conducting this investigation is to identify patterns in logarithmic sequences. Furthermore, after identifying the patterns, one must produce a general statement expressing the general trend within the sequence.

Extracts from this document...

Introduction

International baccalaureate

Mathematics SL

Portfolio Type one

Logarithm bases

CANDIDATE NAME                : Shilpi Singhvi

CANDIDATE NUMBER        :

SCHOOL NAME                        : GANDHI MEMORIAL INT’L SCHOOL

SCHOOL CODE                        : 000902

SESSION                                : MAY 2010

Logarithm Bases

INTRODUCTION

The reasoning behind conducting this investigation is to identify patterns in logarithmic sequences. Furthermore, after identifying the patterns, one must produce a general statement expressing the general trend within the sequence. Once forming a general statement, one must be able to rewrite logarithms in the form of a fraction. This investigation tests the acquired knowledge of logarithms by testing the general statement using various values, forming limitations, and proving scopes. In addition, further investigation may be conducted through the use of graphs, tables of values, and charts.

This assignment is looking for a formula that will give the nthterm for the sequence.

This table gives the next two terms of each sequence.

 nth sequence(1) sequence(2) sequence(3) sequence(4) 1 log8 log81 log25 logm 2 log8 log81 log25 logm 3 log8 log81 log25 logm 4 log8 log81 log25 logm 5 log8 log81 log25 logm 6 log8 log81 log25 log m 7 log8

Middle

m= k/6

Thus the nth term is  where p is k and q is n.

Describing how we obtain log(64) from log(64) and log(64).

In order to obtain the answer of the third logarithm, the product of the first and second logarithms must be divided by the sum of the answers of the first and second logarithms.

log(x), log(x)        log(x)

We use the formula:

logb =

log(x) =          log4 = [1]

log(x) =          log8 = [2]

log4 + log8 =  +

And we have:

log32 =

Therefore the formula we obtain:

log(x) =orlog(x) =

By replacing the value of x = 64 we get,

log(64) =

log(64) = 3 & log(64) = 2        (using GDC)

Thus, log(64) =

Describing how we obtain log(49) from log(49) and log(49).

Thus by using the above formula above:

log(x) =

log(49) =log(49) log(49)

log(49) + log(49)

Solving the equations,

log(49) = 1

log(49) = 2

Therefore,log(49) =

Describing how we obtain log (125) from log (125) and log (125).

Thus, by using the formula

log(x) =,

log (125)   =

+

Solving the equations

log (125) & log (125) by change of base log

= -3= -1

Therefore,

Conclusion

(x) and used log10ab = log10 a + log 10 b in the denominator.

Now by simplifying loga  x= c and logb x = d  by changing the base logs by the formula above and making loga  x and logb x as the subject of the formula and substituting in the first part we get the general statement as .

2nd way:

We simplified the statement logab x by making the bases similar.

Now in the equations loga  x= c and logb x = d  we used the formula to make the bases similar i.e.  and making loga x and logb x as the subject of the formula.

Then we substituted it in the simplified version of logab x . By substituting the values we get the general statement.

Through this general statement we can find out the value of the third term in a sequence when the first two terms are given.

Conclusion

In conclusion, after applying the given knowledge of logarithms, a general statement was formed to prove the validity of various sequences. Also through the use of technology, general statements were proven and theories were confirmed.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## In this investigation I will be examining logarithms and their bases. The purpose of ...

= log381 Y = q(x), where q(x) = log981 Y = r(x), where r(x) = log2781 These graphs also support the expression and the points of intersection also fit the theory mentioned above. Figure 1.3 shows 4 graphs and its points of intersection Y = f(x), where f(x)

2. ## Logarithms. In this investigation, the use of the properties of ...

the values of the next two terms are is by using the formula logmnmk where m is the base and number (constant number), k is the exponent in which m is raised, and n is the term number log28 = log21(23)

1. ## Math Investigation - Properties of Quartics

-69 -395 0 The cubic is therefore 3 + 72 - 69 395 = 0 Second division by the root of point Q (-2) will give us a quadratic -5 1 7 -69 -395 -5 -10 395 1 2 -79 0 The quadratic is therefore 2 + 2 - 79

2. ## This essay will examine theoretical and experimental probability in relation to the Korean card ...

x P(player 2 getting any cards excluding January with?) x P(player 1 getting January with?) x P(player 2 getting any card) = (2/20) x (18/19) x (1/18) x (17/17) = 1/190 P(all) = P(a) + 2P(b) = 1/95+ 1/190 = 0.0157894737 Ddaeng Ddaeng is when a player gets any same months, October is highest and January is lowest.

1. ## The purpose of this investigation is to create and model a dice-based casino game ...

is ; therefore, if the fee to play is x and the payoff offered by the casino is 1.4x, the casino would just break even in the long term. Therefore, the payoff should be under 140% of the fee to play so that the casino stands to profit.

2. ## Math IA patterns within systems of linear equations

To prove this conjecture we consider a general 2 x 2 system of linear equations: (first term: a, common difference: d) (first term: b, common difference: e) In order to solve these simultaneous equations by elimination, we need to multiply the first equation by b and the second equation by a.

1. ## I am going to go through some logarithm bases, by continuing some sequences and ...

To do this I will change the first set of logarithms , so there is an example of a positive, negative, fraction and decimal in place of the x and then the a. log464= log864= log3264= From this we already know that positive numbers will work.

2. ## The purpose of this investigation is to explore the various properties and concepts of ...

Now, a message, written in English, was created. The message chosen is ?IONCANNONREADY?, a quote from the Command and Conquer game series, the ion cannon fires charged particles and causes devastating damage to the enemy base. This message translates to the corresponding numeric code using the system above : 18,3,1 ,6,2,1,1,3,1, 9,10,2,8,23.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to