Logarithms: Finding x - Using Logarithms - Numbas at mathcentre.ac.uk

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3 years, 8 months ago

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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	17/04/2025 09:02
CA10 Logs - Solving equations using logs	Ready to use	Megan Oliver	17/04/2025 09:02

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Question statement

Solve for $x$ :

$\var{a}^x = \var{b} \,.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	2
sol	number	0.50

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Generated value: `integer`

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Advice

To solve $\var{a}^x = \var{b}$ for $x$ , since $x$ is the exponent we want to make use of the following logarithm rule:

$\log(a^n) = n \log(a)$ .

By taking the logarithm of each side and applying the above rule:

$\begin{split}\var{a}^x &\,= \var{b} \\ \log_{10}(\var{a}^x) & \,= \log_{10}(\var{b})\\ x \log_{10}(\var{a}) &\,= \log_{10}(\var{b}) \\\\ x&\,=\simplify{log({b})/log({a})} \\\\ x &\,= \var{sol} \text{ (2 d.p.)}. \end{split}$

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Logarithms: Finding x - Using Logarithms

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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: Finding x - Using Logarithms

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

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`