Ida's copy of Simplify logarithms

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Ida Landgärds

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Ida Landgärds 6 years, 10 months ago

Created this as a copy of Simplify logarithms.

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

Finn $\alpha$ og $\beta$ .

Vi har disse reglene, som gjelder for alle tall $b$ og alle positive tall $x$ og $y$ :

$\begin{align}\log_a(x^b)&=b\log(x)\\ \log_a(x)+\log_a(y)&=\log_a(xy)\text{,}\\ \log_a(x)-\log_a(y)&=\log_a\left(\frac{x}{y}\right)\text{.} \end{align}$

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	3
d	integer	-4
f	decimal	dec("3")
s1	integer	1
s4	integer	-1
a1	integer	7
a2	integer	28
b1	integer	11
b2	integer	9

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)

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Description

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

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

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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Part	Test	Passed?
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Number entry
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Ida Landgärds 6 years, 10 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Ida's copy of Simplify logarithms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ida Landgärds 6 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`