Using Laws for Addition and Subtraction of Logarithms

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From users who are members of Transition to university :

Chris Graham	said	Ready to use	7 years, 7 months ago
Hannah Aldous	said	Needs to be tested	7 years, 8 months ago
Elliott Fletcher	said	Has some problems	7 years, 8 months ago
Christian Lawson-Perfect	said	Has some problems	7 years, 8 months ago

From users who are not members of Transition to university :

Mohini Chand

said

Ready to use

6 years, 8 months ago

History

○

Mohini Chand 6 years, 8 months ago

Gave some feedback: Ready to use

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Chris Graham 7 years, 7 months ago

Gave some feedback: Ready to use

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Chris Graham commented 7 years, 7 months ago

This question had an unwieldy part b), asking the student to simplify an expression containing many log terms. This was set up in an extraordinarily complicated way with over a dozen variables and, as I'm sure we have other similar questions written in a less complex way, I have removed it and reorganised part a) to become two parts. The question is very straightforward now, but I think that's OK.

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Aiden McCall 7 years, 8 months ago

Saved a checkpoint:

Edited some of the advice and added the simplified answer to the advice (with visibility so if gcd of the numerator and denominator = 1 it will only show that and not try to simplify).

Restore this checkpoint

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Has some problems

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Elliott Fletcher commented 7 years, 8 months ago

This looks like a good question i just have a few comments.

In the statement you might need to have a comma after you state the first law of logarithms.

Main Parts

a) good

b) are you wanting the student to input their answer as a simplified fraction or just any fraction? you might need to put in a precision restriction.

Advice

a) i) good, just a typo "subsituting" should be "substituting".

a) ii) same typo as in a) i)

I think the have typed up the wrong questions for the advice here, i'm not sure where the a) ii) part fits in

I think the advice for a) iii) is meant to be for question a) ii) but the numbers here aren't the same as in the question.

Also you have two a) iii)s in the advice, but there are only two questions in part a) in the actual question.

b) i) you might need a full stop after the first line of maths here.

b) ii) again you might need a full stop after the first line of maths.

One of the logs here is in italics as well whereas the others aren't.

Also the final answer in the advice here is not given as a simplified fraction.

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 8 months ago

Part b) asks for the answers as a fraction, but the gaps do not accept fraction input. In addition, the correct answer is displayed as a decimal. Tick the "Allow the student to enter a fraction?" checkbox, which will also reveal an option to display the answer as a fraction.

In the advice, rather than (...), use \left( and \right) for parentheses, which scale to the height of the contents.

The pairs (i),(ii) and (iii),(iv) in part a) don't really ask anything different, but I think that's OK. You could have (iv) result in a fraction, though then you will need to add "Enter your answer as a fraction where appropriate" or similar in the part prompt.

Otherwise this is good.

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

The gaps should be number entry parts, not mathematical expressions.

Restore this checkpoint

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Hannah Aldous 7 years, 8 months ago

Created this as a copy of Combining Logarithm Rules to Solve Equations.

Name	Status	Author	Last Modified
Combining Logarithm Rules to Solve Equations	Ready to use	Hannah Aldous	20/11/2019 14:34
Using Laws for Addition and Subtraction of Logarithms	Ready to use	Hannah Aldous	20/11/2019 14:44
Rearranging Logarithms involving Indices	Ready to use	Hannah Aldous	20/11/2019 14:44
Addition and Subtraction of Logarithms	Ready to use	Adrian Jannetta	16/08/2023 14:56
MATH6058 Addition and Subtraction of Logarithms	draft	Catherine Palmer	09/10/2017 11:30
Raphael's copy of Rearranging Logarithms involving Indices	draft	Raphael Stuhlmeier	27/11/2017 16:06
Addition and Subtraction of Logarithms	draft	Ida Landgärds	16/04/2018 10:43
Ida's copy of Rearranging Logarithms involving Indices	Ready to use	Ida Landgärds	09/05/2018 06:55
spørsmål 3	draft	Ida Landgärds	02/12/2020 15:42
Jonathan's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Jonathan Kress	07/06/2018 01:10
Jeanne's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Jeanne Parmentier	20/07/2018 09:31
Using Laws for Addition and Subtraction of Logarithms [L6 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 11:08
Rearranging Logarithms involving Indices [L6]	draft	Abbi Mullins	24/07/2018 14:39
logarithms addition/subtraction [L6]	draft	Abbi Mullins	24/07/2018 14:49
NUMBAS-Logarithms (laws)	Ready to use	Katy Dobson	30/07/2018 10:39
David's copy of Using Laws for Addition and Subtraction of Logarithms	Ready to use	David Martin	21/09/2018 11:50
David's copy of Combining Logarithm Rules to Solve Equations	draft	David Martin	30/07/2018 14:34
David's copy of Rearranging Logarithms involving Indices	Ready to use	David Martin	17/10/2019 07:25
Joël's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Jo Cohen	02/12/2020 15:42
Blathnaid's copy of spørsmål 3	draft	Blathnaid Sheridan	02/12/2020 15:42
cormac's copy of Ida's copy of Rearranging Logarithms involving Indices	draft	cormac breen	05/11/2018 13:37
cormac's copy of Ida's copy of Rearranging Logarithms involving Indices	draft	cormac breen	05/11/2018 13:38
cormac's copy of Ida's copy of Rearranging Logarithms involving Indices	draft	cormac breen	05/11/2018 13:54
Justin's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Justin McGuinness	14/05/2019 14:55
Maria's copy of Rearranging Logarithms involving Indices	draft	Maria Aneiros	11/06/2019 05:32
Maria's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Maria Aneiros	11/06/2019 05:30
Maria's copy of Combining Logarithm Rules to Solve Equations	draft	Maria Aneiros	25/05/2019 08:02
Using Laws for Addition and Subtraction of Logarithms	draft	Xiaodan Leng	10/07/2019 23:28
Logarithms (laws)	draft	Xiaodan Leng	10/07/2019 23:57
Using Laws for Addition and Subtraction of Logarithms	draft	Xiaodan Leng	11/07/2019 00:00
Addition and Subtraction of Logarithms	draft	Xiaodan Leng	11/07/2019 00:15
Rearranging Logarithms involving Indices	draft	Xiaodan Leng	11/07/2019 00:16
Combining Logarithm Rules to Solve Equations	draft	Xiaodan Leng	11/07/2019 01:39
Katy's copy of Combining Logarithm Rules to Solve Equations	draft	Katy Dobson	03/09/2019 08:29
Katy's copy of Using Laws for Addition and Subtraction of Logarithms	draft	Katy Dobson	03/09/2019 08:29
Musa's copy of 3 Addition and Subtraction of Logarithms	draft	Musa Mammadov	27/06/2023 01:29
Rearranging Logarithms involving Indices	Ready to use	Wan Mekwi	13/10/2020 13:19
Combining Logarithm Rules to Solve Equations	Ready to use	Wan Mekwi	13/10/2020 13:22

There are 84 other versions that do you not have access to.

Question statement

Simplify the expressions to fill in the gaps.

Give any introductory information the student needs.

			Name	Type	Generated Value

			x1	list	[ 15, 9, 10, 5, 16, 10, 7, 2 ]
			y1	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(2..20),8)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 15, 9, 10, 5, 16, 10, 7, 2 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Number entry
  Add
1. Step Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\log_a(\var{x1[1]})+ \log_a(\var{x1[0]})=\log_a($ Unnamed gap $)$

Advice

a)

We need to use the rule

$\log_a(x)+\log_a(y)=\log_a(xy)\text{.}$

Substituting in our values for $x$ and $y$ gives

$\begin{align} \log_a(\var{x1[1]})+\log_a(\var{x1[0]})&=\log_a(\var{x1[1]}\times \var{x1[0]})\\ &=\log_a(\var{x1[1]*x1[0]})\text{.} \end{align}$

b)

We need to use the rule

$\log_a(x)-\log_a(y)=\log_a\left(\frac{x}{y}\right)\text{.}$

Substituting in our values for $x$ and $y$ gives

$\begin{align} \log_a(\var{x1[4]*y1})-\log_a(\var{x1[4]})&=\log_a(\var{x1[4]*y1}\div \var{x1[4]})\\ &=\log_a(\var{y1})\text{.} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only

This question is used in the following exams:

Logarithms by Christian Lawson-Perfect in Transition to university.
Joshua's copy of Printable assignment using NUMBAS by Joshua Capel in Joshua's workspace.
franco's copy of Joshua's copy of Printable assignment using NUMBAS by franco chooramen in franco's workspace.
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Using Laws for Addition and Subtraction of Logarithms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mohini Chand 6 years, 8 months ago

Chris Graham 7 years, 7 months ago

Chris Graham commented 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

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Error

Using Laws for Addition and Subtraction of Logarithms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mohini Chand 6 years, 8 months ago

Chris Graham 7 years, 7 months ago

Chris Graham commented 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

Generated value: `list`