Logarithms: Expanding Expressions 1

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Name	Status	Author	Last Modified
Logarithms: Expanding Expressions 1	Ready to use	Ben McGovern	10/10/2022 12:55
Logarithms: Expanding Expressions 2	Ready to use	Ben McGovern	10/10/2022 12:55
Logarithms: Expanding Expressions 3	Ready to use	Ben McGovern	10/10/2022 12:55
Logarithms: Expanding Expressions 4	Ready to use	Ben McGovern	10/10/2022 12:55

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Question statement

Rewrite the following expression in terms of $\simplify{log({a})}$ and $\simplify{log({b})}$ :

$\simplify{log({a^n * b})}.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
b	integer	5
n	integer	3

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1. Gap Mathematical expression
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Unnamed gap

Advice

To rewrite $\simplify{log({a^n*b})}$ in terms of $\simplify{log({a})}$ and $\simplify{log({b})}$ , we want to use the following logarithm rules:

$\simplify{log(a*b) = log(a)+log(b)}$ ;
$\simplify{log(a^n) = n*log(a)}$ .

Firstly, we want to express $\var{a^n*b}$ in terms of $\var{a}$ and $\var{b}$ :

$\begin{split} \var{a^n*b} &\,= \var{a^n} \times \var{b} \\ &\,= \var{a}^\var{n} \times \var{b}. \end{split}$

Therefore,

$\begin{split} \simplify{log({a^n*b})} &\,= \simplify[!collectNumbers]{log({a}^{n} * {b})} \\ &\,= \simplify[!collectNumbers]{log({a}^{n})+log({b})} \\ &\,= \simplify{{n}log({a})+log({b})} .\end{split}$

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Taxonomy: mathcentre

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Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 3 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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Logarithms: Expanding Expressions 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 3 years, 10 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`