Simplify logarithms 1: (Video)

Error

There was an error loading the page.

Contributors

Bill Foster

History

○

Bill Foster 55 years, 2 months ago

Created this.

There is only one version of this question that you have access to.

There are 5 other versions that do you not have access to.

Question statement

Answer the following questions on logarithms.

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	3
d	integer	-5
f	decimal	dec("2")
s1	integer	-1
s4	integer	-1
a1	integer	-6
a2	integer	9
b1	integer	6
b2	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)

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`

→ Used by:

Advice
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Express the following in terms of $\log_a(x)$ and $\log_a(y)$

$\log_a(x^{\var{a1}}y^{\var{b1}})=\alpha\log_a(x)+\beta\log_a(y)$

$\alpha=\;\;$ Gap 0., $\beta=\;\;$ Gap 1.

In Show steps you will find a video explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Advice

The rules for combining logs are

$\begin{eqnarray*} \log_a(bc)&=&\log_a(b)+\log_a(c)\\ \\ \log_a\left(\frac{b}{c}\right)&=&\log_a(b)-\log_a(c)\\ \\ \log_a(b^r)&=&r\log_a(b) \end{eqnarray*}$

a)
Using these rules gives:

$\begin{eqnarray*} \log_a(x^{\var{a1}}y^{\var{b1}})&=&\log_a(x^{\var{a1}})+\log_a(y^{\var{b1}})\\ &=&\var{a1}\log_a(x)+\var{b1}\log_a(y) \end{eqnarray*}$

$\begin{eqnarray*} \simplify[std]{{a2}/{b2}}\log_a(x)+\log_a(\simplify{{c}*x+{d}})-\log_a(\simplify{x^(1/{b2})})&=&\log_a(x^\frac{\var{a2}}{\var{b2}})+\log_a(\simplify{{c}*x+{d}})-\log_a(\simplify{x^(1/{b2})})\\ \\ &=&\log_a\left(\simplify[std]{(x^({a2}/{b2})*({c}x+{d}))/(x^(1/{b2}))}\right)\\ &=&\log_a\left(\simplify{x^{f}*({c}x+{d})}\right) \end{eqnarray*}$

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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Simplify logarithms 1: (Video)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`