Enrol now for our new online tutoring program. Learn from the best tutors. Get amazing results. Learn more.

March 05, 2021, 12:14:59 am

### AuthorTopic: log question, posssibly considered ambigous?  (Read 1429 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

#### almostatrap

• Victorian
• Forum Regular
• Posts: 96
##### log question, posssibly considered ambigous?
« on: November 06, 2009, 12:00:34 pm »
so x=-1 is not valid. and 2ln(x) does not always = ln(x^2)

I just went through the year 11 and 12 essentials textbooks, and nowhere does it mention exceptions to log laws. Even searching the internet i couldn't find it. And i have never been taught it (my teacher is awesome).

So we're just meant to know intuitively that log laws are not valid in this situation?

I declare question 9 ambiguous! marks for everyone!

I doubt this will be the case, but yeah.

what do people think?
biology [38], specialist [39], methods [43], english [38], physics [42], philosophy [33]

enter: 97.70

#### TrueTears

• TT
• Honorary Moderator
• Great Wonder of ATAR Notes
• Posts: 16362
##### Re: log question, posssibly considered ambigous?
« Reply #1 on: November 06, 2009, 12:01:58 pm »
I said the domain is the intersection of the two functions.

For y = 2ln(x) the domain is x > 0

For y = ln(x+3) the domain is x>-3

Thus the domain is x>0

Since -1<0

We only take $\frac{3}{2}$
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

#### simpak

• Victorian
• ATAR Notes Legend
• Posts: 3587
##### Re: log question, posssibly considered ambigous?
« Reply #2 on: November 06, 2009, 12:02:41 pm »
I assumed that the negative answer I got couldn't be right because then you would be taking the log of a negative.
BUT, the negative answer I got was not -1 because I made a silly mistake.
Still, same logic.
2009 ENTER: 99.05
2014: BSci Hons (Microbiology/Immunology) at UoM
2015+: PhD (Immunology) at UoM

#### nala

• Victorian
• Trailblazer
• Posts: 45
##### Re: log question, posssibly considered ambigous?
« Reply #3 on: November 06, 2009, 12:06:13 pm »
I figured that rather than putting the 2 above the x, say you divided the other logs by 2 instead. You are left with loge(-1), therefore it is undefined.

#### [email protected]

• Victorian
• ATAR Notes Legend
• Posts: 4324
• School: Heatherton Christian College
##### Re: log question, posssibly considered ambigous?
« Reply #4 on: November 06, 2009, 12:07:28 pm »
You have to see whether the solutions are defined in the original unaltered expression.
2009/2010: Mathematical Methods(non-CAS) ; Business Management | English ; Literature - Physics ; Chemistry - Specialist Mathematics ; MUEP Maths

96.85

2011-2015: Bachelor of Aerospace Engineering and Bachelor of Science, Monash University

2015-____: To infinity and beyond.

#### almostatrap

• Victorian
• Forum Regular
• Posts: 96
##### Re: log question, posssibly considered ambigous?
« Reply #5 on: November 06, 2009, 12:08:20 pm »
all good points! oh well
biology [38], specialist [39], methods [43], english [38], physics [42], philosophy [33]

enter: 97.70

#### TrueTears

• TT
• Honorary Moderator
• Great Wonder of ATAR Notes
• Posts: 16362
##### Re: log question, posssibly considered ambigous?
« Reply #6 on: November 06, 2009, 12:09:33 pm »
so x=-1 is not valid. and 2ln(x) does not always = ln(x^2)

I just went through the year 11 and 12 essentials textbooks, and nowhere does it mention exceptions to log laws. Even searching the internet i couldn't find it. And i have never been taught it (my teacher is awesome).

So we're just meant to know intuitively that log laws are not valid in this situation?

I declare question 9 ambiguous! marks for everyone!

I doubt this will be the case, but yeah.

what do people think?
Also remember squaring a number leads to redundant solutions.

$x^2 = 4$

$x = \pm 2$

However if you had $x = \sqrt{4}$ you'd only be left with the positive answer $x = 2$.

Same logic applies, squaring the x leads to the redundant solution of x = 1.
« Last Edit: November 06, 2009, 01:36:25 pm by TrueTears »
PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

#### NE2000

• Victorian
• Part of the furniture
• Posts: 1221
• living an alternate reality
##### Re: log question, posssibly considered ambigous?
« Reply #7 on: November 06, 2009, 12:38:54 pm »
It's a good habit to define domains (at least in your head) before you attempt a question.
2009: English, Specialist Math, Mathematical Methods, Chemistry, Physics

#### lilyrose

• Victorian
• Forum Regular
• Posts: 61
##### Re: log question, posssibly considered ambigous?
« Reply #8 on: November 06, 2009, 01:10:30 pm »
do you get marks off if you forgot to simplfy things?
also, i forgot to include units for rate of change and i accidently left the -ve value forlog...is that -1 mark each??

#### NE2000

• Victorian
• Part of the furniture
• Posts: 1221
• living an alternate reality
##### Re: log question, posssibly considered ambigous?
« Reply #9 on: November 06, 2009, 01:11:40 pm »
In spesh the assessment reports say that you must simplify. But I haven't seen that in a methods one so maybe not simplifying it completely will not be penalized

The units for rate of change, the question specifically asked you to put units so not sure. And the -ve value for log is an incorrect answer
2009: English, Specialist Math, Mathematical Methods, Chemistry, Physics

#### tomygun_123

• Victorian
• Trailblazer
• Posts: 46
##### Re: log question, posssibly considered ambigous?
« Reply #10 on: November 06, 2009, 01:20:25 pm »
you can only take x>3/2 since it wasnt an absolute function, also taking the square of 1 will give you +- answers therefore you must reject the negative... i would think that this was just common sense since bodmas clearly applies within the brackets. But i guess it could have been a bit ambiguous.
(2009):
Physics _
Specialist Mathematics _
Mathematical Methods _
English _
Chemistry _

ENTER: 95...?? still a few months to go...

#### lilyrose

• Victorian
• Forum Regular
• Posts: 61
##### Re: log question, posssibly considered ambigous?
« Reply #11 on: November 06, 2009, 01:25:36 pm »
In spesh the assessment reports say that you must simplify. But I haven't seen that in a methods one so maybe not simplifying it completely will not be penalized

The units for rate of change, the question specifically asked you to put units so not sure. And the -ve value for log is an incorrect answer

well i accidently forgot to disregard the -ve.. i still had the 3/2.. would i get one mark off for including that x=-1?

so annoyed, i made sososososo many stupid mistakes