Solving equations using log

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Xiaodan Leng 5 years, 9 months ago

Created this as a copy of Solving equations using log.

Name	Status	Author	Last Modified
Solving equations using log	Has some problems	joshua boddy	12/11/2020 14:02
Numerical Skills - Solving equations using log	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills - Solving equations using log summative	Ready to use	Jinhua Mathias	28/08/2024 12:15
Solving equations using log	draft	Xiaodan Leng	11/07/2019 06:35

Question statement

Solve each of the following equations for $x$ , giving your answers in terms of base 10 logarithms OR to 3 decimal places.

Remember to write $\simplify{log(a)}$ you must type loga with brackets around the a.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	9
a2	integer	4
b1	integer	8
b2	integer	2
c1	integer	2
c2	integer	6
d1	integer	5
d2	integer	6
e1	integer	6
e2	integer	2
e3	integer	2
e4	integer	-2
e5	integer	1
e6	integer	1
f1	integer	9
f2	integer	6
f3	integer	1
f4	integer	3
f5	integer	3
Unnamed

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..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:

"Part a)" - prompt
"Part a)" → "Gap 1." - Correct answer

Parts

Part a) Gap-fill
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
Part e) Gap-fill
1. Gap Mathematical expression
  Add
Part f) 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.

$\var{a1}^x = \var{a2}$

$x=$ $\log_{10}$ Gap 0. $\log_{10}$ Gap 1.

$x=\log_{\var{a1}}$ Gap 2.

Advice

To solve this type of question, we want to take logarithms of both sides of the equation in order to try to isolate x.

For example, if we have $a^x = b$ then we proceed as above to get $x\log{a} = \log{b}$ and hence $x = \frac{\log{a}}{\log{b}}$

Laws of logarithms are useful here:

$\log{a} + \log{b} = \log{ab}$

$\log{a} - \log{b} = \log{\frac{a}{b}}$

$\log{a^n} = n\log{a}$

Give a worked solution to the whole question.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Solving equations using log

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

Generated value: `integer`