Logarithms: Solving equations 3

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Introduction to Calculus :

Wan Mekwi

said

Ready to use

4 years, 6 months ago

History

○

Wan Mekwi 4 years, 6 months ago

Published this.

○

Wan Mekwi 4 years, 6 months ago

Gave some feedback: Ready to use

○

Wan Mekwi 4 years, 6 months ago

Created this as a copy of Logarithms: Solving equations 3.

Name	Status	Author	Last Modified
Logarithms: Solving equations 3	draft	Bill Foster	06/08/2020 08:42
Logarithms: Solving equations 3	Ready to use	Wan Mekwi	13/10/2020 13:21

There are 12 other versions that do you not have access to.

Question statement

Solve the following equation for $x$ .

$\simplify[std]{log({a1}x+{b1})-log({c1}x+{d1})={e1}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

e1	integer	2
a1	integer	2
b1	integer	15
tol	integer	0
ans	number	-0.492
c1	integer	18
tans	number	-0.4922135706
d1	integer	9

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..2)

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:

tans

Statement
Advice

Parts

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.

Input the solution for $x$ here:

$x=\;\;$ Unnamed gap

Input your answer to 3 decimal places.

Advice

First use one of the logarith laws which states (for logarithms to any base)

$\log(a)-\log(b)=\log\left(\frac{a}{b}\right)$

So the equation can be written as:

$\log_{10}\left(\simplify[std]{({a1}x+{b1})/({c1}x+{d1})}\right)=\var{e1}$
Now exponentiate both sides to get:

$\simplify[std,!otherNumbers]{({a1}x+{b1})/({c1}x+{d1})}=10^{\var{e1}} \Rightarrow \simplify[std,!otherNumbers]{{a1}x+{b1}=10^{e1}({c1}x+{d1})}$
Collect together terms in

$x$ on the left and everything else on the right of the equation gives:

$\simplify[std,!otherNumbers]{x({a1}-10^{e1}*{c1})=10^{e1}*{d1}-{b1}}$
Finally rearrange to get:

$\simplify[std]{x=(10^{e1}*{d1}-{b1})/({a1}-10^{e1}*{c1})={10^e1*d1-b1}/{a1-10^e1*c1}}$
which to 3 decimal places evaluates to

$x=\var{ans}.$

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

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Wan Mekwi 4 years, 6 months ago

Wan Mekwi 4 years, 6 months ago

Wan Mekwi 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Logarithms: Solving equations 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Wan Mekwi 4 years, 6 months ago

Wan Mekwi 4 years, 6 months ago

Wan Mekwi 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`