Simplify logarithms

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Bill Foster

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6 years, 4 months ago

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Bill Foster 6 years, 4 months ago

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Name	Status	Author	Last Modified
Simplify logarithms	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Simplify logarithms	draft	Ida Landgärds	16/04/2018 10:48
Ida's copy of Simplify logarithms	draft	Ida Landgärds	02/05/2018 09:38
Blathnaid's copy of Simplify logarithms	draft	Blathnaid Sheridan	17/10/2019 20:04
Blathnaid's copy of Simplify logarithms	draft	Blathnaid Sheridan	05/10/2018 20:30
cormac's copy of Blathnaid's copy of Simplify logarithms	draft	cormac breen	30/10/2018 15:50
Simplify logarithms	draft	Xiaodan Leng	10/07/2019 22:45
Logarithms	draft	Leonardo Juliano	21/11/2024 13:31
Simplify logarithms	Ready to use	Wan Mekwi	13/10/2020 13:20

There are 21 other versions that do you not have access to.

Question statement

Answer the following questions on logarithms.

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	5
d	integer	-2
f	decimal	dec("2")
s1	integer	1
s4	integer	-1
a1	integer	2
a2	integer	7
b1	integer	6
b2	integer	3

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Value

xxxxxxxxxx
 
random(1..9)

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Description

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Generated value: `integer`

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Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Part b) Gap-fill
1. Gap Mathematical expression
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Gap-fill

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

Express the following in terms of $\log_a(x)$ and $\log_a(y)$

$\log_a(x^{\var{a1}}y^{\var{b1}})=\alpha\log_a(x)+\beta\log_a(y)$

$\alpha=\;\;$ Gap 0., $\beta=\;\;$ Gap 1.

Advice

The rules for combining logs are

$\begin{eqnarray*} \log_a(bc)&=&\log_a(b)+\log_a(c)\\ \\ \log_a\left(\frac{b}{c}\right)&=&\log_a(b)-\log_a(c)\\ \\ \log_a(b^r)&=&r\log_a(b) \end{eqnarray*}$

a)
Using these rules gives:

$\begin{eqnarray*} \log_a(x^{\var{a1}}y^{\var{b1}})&=&\log_a(x^{\var{a1}})+\log_a(y^{\var{b1}})\\ &=&\var{a1}\log_a(x)+\var{b1}\log_a(y) \end{eqnarray*}$

$\begin{eqnarray*} \simplify[std]{{a2}/{b2}}\log_a(x)+\log_a(\simplify{{c}*x+{d}})-\log_a(\simplify{x^(1/{b2})})&=&\log_a(x^\frac{\var{a2}}{\var{b2}})+\log_a(\simplify{{c}*x+{d}})-\log_a(\simplify{x^(1/{b2})})\\ \\ &=&\log_a\left(\simplify[std]{(x^({a2}/{b2})*({c}x+{d}))/(x^(1/{b2}))}\right)\\ &=&\log_a\left(\simplify{x^{f}*({c}x+{d})}\right) \end{eqnarray*}$

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Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Simplify logarithms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`