Logs: scalar multiple to power inside

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Ben Brawn

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From users who are members of post-algebra Arithmetic and Numeracy :

Ben Brawn

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9 years, 1 month ago

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Ben Brawn commented 3 years, 3 months ago

removed the steps which just said which formula to use, and added worked solution to the advice section.

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Ben Brawn 9 years, 1 month ago

Gave some feedback: Ready to use

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Ben Brawn 9 years, 4 months ago

Created this.

Name	Status	Author	Last Modified
Logs: scalar multiple to power inside	Ready to use	Ben Brawn	16/12/2021 13:25
Logs: addition to multiplication inside	Ready to use	Ben Brawn	16/07/2018 04:19
Logs: subtraction to division inside	Ready to use	Ben Brawn	02/06/2016 06:49
Marta's copy of Logs: addition to multiplication inside	Ready to use	Marta S	01/06/2016 09:47
Marta's copy of Logs: addition to multiplication inside	Ready to use	Marta S	01/06/2016 09:47
David's copy of Logs: subtraction to division inside	Ready to use	David Martin	21/09/2018 11:54
David's copy of Logs: addition to multiplication inside	Ready to use	David Martin	21/09/2018 11:52
David's copy of Logs: scalar multiple to power inside	Ready to use	David Martin	21/09/2018 11:31
Harry's copy of David's copy of Logs: addition to multiplication inside	draft	Harry Flynn	15/11/2018 10:36
Harry's copy of David's copy of Logs: subtraction to division inside	draft	Harry Flynn	15/11/2018 10:37
David's copy of Logs: subtraction to division inside	draft	Xiaodan Leng	10/07/2019 23:28
Logs: addition to multiplication inside	draft	Xiaodan Leng	10/07/2019 23:28
Logs: addition to multiplication inside	draft	Xiaodan Leng	10/07/2019 23:58
Logs: scalar multiple to power inside	draft	Xiaodan Leng	11/07/2019 06:09
Logs: subtraction to division inside	draft	Xiaodan Leng	11/07/2019 06:10

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Question statement

Determine the following (if necessary use ^ to indicate exponents, e.g. 2^(16) indicates $2^{16}$ ):

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	-11
power	integer	-4
ans1	integer	44
mult	integer	3
d	integer	2
root	integer	5
square	number	16
ans4	number	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-12..12 except [0,1])

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-11

→ Used by:

ans1
d

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
1. Gap Mathematical expression
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Part c) Gap-fill
1. Gap Number entry
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Part d) Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Suppose $\log_b\left(a\right)=\var{c}$ . Evaluate $\log_b\left(a^\var{power}\right)$ = Unnamed gap.

Advice

$\begin{align*}\log_b\left(a^\var{power}\right) &= \var{power}\log_b\left(a\right)&& \text{(by the log law }\log_b(a^n)=n\log_b(a)\text{)}\\ &=\var{power}\times \var{c}&& \text{(given)}\\&=\var{power*c} \end{align*}$

$\begin{align*}\var{mult}\log_b\left(a\right) &=\log_b\left(a^\var{mult}\right)&& \text{(by the log law }\log_b(a^n)=n\log_b(a)\text{)} \end{align*}$

$\begin{align*}\log_b\left(\sqrt[\var{root}]{x}\right) &=\log_b\left(x^{\frac{1}{\var{root}}}\right)&& \text{(by the index law }\sqrt[n]{x}=x^{\frac{1}{n}}\text{)}\\[3pt] &=\frac{1}{\var{root}}\log_b(x)&& \text{(by the log law }\log_b(a^n)=n\log_b(a)\text{)}\\[3pt]&=\frac{1}{\var{root}}\times \var{d} &&\text{(given)}\\[3pt]&=\simplify{{d}/{root}}\end{align*}$

$\begin{align*}\frac{1}{2}\log_b\left(\var{square}\right)&=\log_b\left(\var{square}^{\frac{1}{2}}\right) &&\text{(by the log law }\log_b(a^n)=n\log_b(a)\text{)} \\&=\log_b\left(\sqrt{\var{square}}\right)&& \text{(by the index law }\sqrt[n]{x}=x^{\frac{1}{n}}\text{)}\\[3pt] &=\log_b(\var{ans4})\end{align*}$

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Taxonomy: mathcentre

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Ben Brawn commented 3 years, 3 months ago

Ben Brawn 9 years, 1 month ago

Ben Brawn 9 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Logs: scalar multiple to power inside

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn commented 3 years, 3 months ago

Ben Brawn 9 years, 1 month ago

Ben Brawn 9 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`