Log equation 2

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Martin Jones

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Ready to use

3 years, 3 months ago

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Martin Jones 3 years, 3 months ago

Gave some feedback: Ready to use

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Martin Jones 3 years, 3 months ago

Published this.

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Martin Jones 3 years, 3 months ago

Created this as a copy of Log equation 1.

Name	Status	Author	Last Modified
Log equation 1	Ready to use	Martin Jones	09/02/2023 11:09
Log equation 2	Ready to use	Martin Jones	09/02/2023 11:10

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Question statement

Solve the equation

$\simplify{{B}*log(({A}-x)^2)}=\var{D}$

Give any introductory information the student needs.

			Name	Type	Generated Value

C	integer	3
D	number	10.4
B	integer	13
A	integer	77
x	decimal	dec("7.448811356849041988891496793220067260584e+1")
x2	decimal	dec("7.951188643150958011108503206779932739416e+1")

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Name

Data type

Value

xxxxxxxxxx
 
random(2..10)

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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

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$x=\;$ Gap 0. or $x=\;$ Gap 1.

Advice

Starting from the equation

$\simplify{{B}*log(({A}-x)^2)}=\var{D}$

Divide by $\var{B}$ :

$\simplify{log(({A}-x)^2)}=\frac{\var{D}}{\var{B}}=\var{D/B}$

Take $10$ to the power:

$\simplify{({A}-x)^2}=10^\var{D/B}=\var{10^(D/B)}$

Square root:

$\simplify{{A}-x}=\pm\sqrt{\var{10^(D/B)}}=\pm\var{sqrt(10^(D/B))}$

Subtract from $\var{A}$ :

$x=\var{A}\mp\var{sqrt(10^(D/B))}=\var{x}\text{ or }\var{x2}$

Rounding to 2 decimal places gives $x=\var{precround(x,2)}$ or $x=\var{precround(x2,2)}$

Give a worked solution to the whole question.

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

This question is used in the following exams:

Tess's copy of Equations involving logs by Tess Lynn in Tess's workspace.
Equations involving logs by Tess Lynn in Glasgow Numbas Question Pool.
Outcome 2 revision questions by Martin Jones in Martin's workspace.
Equations involving logs by Martin Jones in Martin's workspace.
Solve equations (incl logs) by Martin Jones in Martin's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Martin Jones 3 years, 3 months ago

Martin Jones 3 years, 3 months ago

Martin Jones 3 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Log equation 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Martin Jones 3 years, 3 months ago

Martin Jones 3 years, 3 months ago

Martin Jones 3 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`