CA9 Logs - rules 1 - Numbas at mathcentre.ac.uk

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From users who are members of Skills Audits for Maths and Stats :

Lauren Desoysa	said	Ready to use	1 year, 1 month ago
Megan Oliver	said	Needs to be tested	1 year, 1 month ago

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Will Morgan 11 months, 2 weeks ago

Published this.

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Lauren Desoysa 1 year, 1 month ago

Gave some feedback: Ready to use

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Megan Oliver 1 year, 1 month ago

Gave some feedback: Needs to be tested

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Megan Oliver 1 year, 1 month ago

Created this as a copy of Logarithms: Solving Logarithmic Equations 6 - Sum of Logarithms.

Name	Status	Author	Last Modified
Logarithms: Finding x - Using Logarithms	Ready to use	Ben McGovern	10/10/2022 12:47
Logarithms: Solving Logarithmic Equations 6 - Sum of Logarithms	Ready to use	Ben McGovern	10/10/2022 12:54
Logarithms: Solving Logarithmic Equations 5	Ready to use	Ben McGovern	10/10/2022 12:54
CA9 Logs - rules 1	Ready to use	Megan Oliver	09/04/2024 15:43
CA10 Logs - Solving equations using logs	Ready to use	Megan Oliver	09/04/2024 15:40

There are 26 other versions that do you not have access to.

Question statement

Solve for $x$ :

$\var{a}\log(x)+\log(\var{b})=\log(\var{c}).$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
b	integer	6
c	integer	26
sol	decimal	dec("1.63")

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1. Gap Mathematical expression
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$x=$ Unnamed gap (Give you answer to 2 decimal places where necessary)

Advice

To solve $\var{a}\log(x)+\log(\var{b})=\log(\var{c})$ for $x$ , we want to use the following logarithm rules:

$\log(a^n) = n\log(a)$ ;
$\log(a)+\log(b) = \log(ab)$ .

Hence,

$\begin{split} \var{a}\log(x)+\log(\var{b}) &\,=\log(\var{c}) \\ \log(x^\var{a})+\log(\var{b}) &\,= \log(\var{c}) \\ \log(\var{b}x^\var{a}) &\,= \log(\var{c}). \end{split}$

If $\log(a)=\log(b)$ then this implies $a=b$ . Therefore,

$\begin{split} \var{b}x^\var{a} &\,=\var{c} \\ x^\var{a} &\,= \simplify[fractionNumbers]{{c/b}} \\ x &\,= \simplify[fractionNumbers]{({c/b})^(1/{a})} \\ x &\,= \var{sol} \text{ (2 d.p.)}\end{split}$

Use this link to find rsources to help you revise how the rules of logarithms to help you solve logarithmic equations.

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CA9 Logs - rules 1

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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CA9 Logs - rules 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Will Morgan 11 months, 2 weeks ago

Lauren Desoysa 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Megan Oliver 1 year, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`