Ugur's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Ugur's workspace :

Ugur Efem

said

Ready to use

3 years, 2 months ago

History

○

Ugur Efem 3 years, 2 months ago

Published this.

○

Ugur Efem 3 years, 2 months ago

Gave some feedback: Ready to use

○

Ugur Efem 3 years, 3 months ago

Created this as a copy of Using the Logarithm Equivalence

$\log_ba=c \Longleftrightarrow a=b^c$ .

Name	Status	Author	Last Modified
Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Hannah Aldous	20/11/2019 14:45
Inbbavathie's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Inbbavathie Ravi	24/07/2017 03:49
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Ida Landgärds	09/05/2018 06:55
spørsmål 2	Ready to use	Ida Landgärds	16/04/2021 05:04
Logarithms [L6]	draft	Abbi Mullins	24/07/2018 14:52
David's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	David Martin	30/07/2018 14:34
Harry's copy of David's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Harry Flynn	15/11/2018 10:33
Basic Algebra : Log	draft	Johnny Yi	23/01/2019 05:00
Maria's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Maria Aneiros	29/05/2019 06:58
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Xiaodan Leng	11/07/2019 00:16
Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	draft	Xiaodan Leng	11/07/2019 01:47
Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Wan Mekwi	13/10/2020 13:19
Ugur's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$	Ready to use	Ugur Efem	12/01/2022 11:45

There are 31 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

g3	integer	4
g2	integer	10
g4	integer	8
g1	integer	2

			Name	Type	Generated Value

			h1	integer	10
			h2	integer	4

			Name	Type	Generated Value

f	integer	5
f2	integer	8
f1	integer	4
f3	integer	7
f4	integer	12
f5	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10except g1 g2)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Choose several from a list

Gap-fill

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

Rearrange the equation to find $x$ .

$\log_\var{f}(x)=\var{f1}$

$x=$ Unnamed gap

Advice

a)

We can rearrange logarithms using indices.

$\log_ba=c \Longleftrightarrow a=b^c$

Using this equivalence we can rewrite $\log_\var{f}x=\var{f1}$ .

$\begin{align} x&= \var{f}^\var{f1} \\ &=\var{f^f1} \end{align}$

b)

We can use the equivalence to rewrite our equation.

$\log_ba=c \Longleftrightarrow a=b^c$

We can write out our values to makes it easier.

$\begin{align} a&=x \\ b&=\var{g1}\\ c&=y+\var{g2} \end{align}$

Then we can write out our equation in the required form.

$x=\var{g1}^{y+\var{g2}}$

c)

We can use the same equivalence as in part b).

$\log_ba=c \Longleftrightarrow a=b^c$

We have

$\begin{align} a&=y+\var{h1} \\ b&=x\\ c&=\var{h2}\text{.} \\ \\ \log_{x}(y+\var{h1}) &= \var{h2} \\ \implies y+\var{h1} &= x^{\var{h2}} \\ x &= (y+\var{h1})^{\frac{1}{\var{h2}}} \end{align}$

d)

The two in this list that don't equal $x$ are $\log_e(x)$ and $\log_{10}(x)$ .

$\begin{align} \log_e(x)&=\ln(x)\\ \log_{10}(x)&=\log(x)\text{.} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose several from a list
Choose several from a list		Hasn't run yet

This question is used in the following exams:

FY001 - 2021 MOCK A by Ugur Efem in Ugur's workspace.
Ugur's copy of FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
Ugur's copy of FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
Ugur's copy of FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
Ugur's copy of FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
Ugur's copy of FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
FY001 - 2021 Exam Extra time by Ugur Efem in Ugur's workspace.
FY001 - 2021 Exam by Ugur Efem in Ugur's workspace.
FY001 - 2021 Referral Exam by Ugur Efem in Ugur's workspace.
test by Carolina Torneiro in Carolina's workspace.
FY001 - 2021 Exam by steve kilgallon in FY001 - Core Mathematics.
FY001 - 2021 Referral - Deferral Exam by steve kilgallon in FY001 - Core Mathematics.

Loading...

Error

Ugur's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

Loading...

Error

Ugur's copy of Using the Logarithm Equivalence logba=c⟺a=bc\log_ba=c \Longleftrightarrow a=b^c

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 2 months ago

Ugur Efem 3 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Ugur's copy of Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$

Generated value: `integer`