Logarithms: Expanding Expressions 4

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3 years, 8 months ago

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Christian Lawson-Perfect 2 years, 7 months ago

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Ben McGovern 3 years, 8 months ago

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Ben McGovern 3 years, 10 months ago

Created this as a copy of Logarithms: Expanding Expressions 2.

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 $\simplify{log({b})}$ :

$\simplify[fractionNumbers]{log(sqrt({a})/ {b^n})}.$

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			Name	Type	Generated Value

a	integer	2
b	integer	7
n	integer	2

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

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

Hence,

$\begin{split} \simplify[fractionNumbers]{log(sqrt({a})/{b^n})} &\,= \simplify{log(sqrt({a})) - log({b^n})} \\ &\,= \simplify[!collectNumbers]{log({a}^(1/2)) - log({b}^{n})} \\ &\,= \simplify{(1/2)log({a})-{n}log({b})} .\end{split}$

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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

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Logarithms: Expanding Expressions 4

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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Generated value: integer

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Gap-fill

Generated value: `integer`