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

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Xiaodan Leng 5 years, 9 months ago

Created this as a copy of 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

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Question statement

Changing the subject of an equation involving logarithms often requires the use of the equivalence

$\log_ba=c \Longleftrightarrow a=b^c\text{.}$

Give any introductory information the student needs.

			Name	Type	Generated Value

g3	integer	9
g2	integer	10
g4	integer	3
g1	integer	3

			Name	Type	Generated Value

			h1	integer	6
			h2	integer	3

			Name	Type	Generated Value

f	integer	9
f2	integer	3
f1	integer	5
f3	integer	6
f4	integer	7
f5	integer	3

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:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) 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.

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

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Error

Logarithm Equivalence logba=c⟺a=bc\log_ba=c \Longleftrightarrow a=b^c

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

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

Generated value: `integer`