VCE Methods Question Thread!

[Bluegirl]

I don't know how you can have x=1 in the ln but anyway... I'll assume you meant minus

Ln(3x-2/x-1) = 0
3x-2 / x-1 = e^0
3x-2 / x-1 = 1
3x-2 = x-1
2x = 1
x = 1/2

Woops, typo! Thankyou!

[b^3]

I don't know how you can have x=1 in the ln but anyway... I'll assume you meant minus

Ln(3x-2/x-1) = 0
3x-2 / x-1 = e^0
3x-2 / x-1 = 1
3x-2 = x-1
2x = 1
x = 1/2

Just hold up a min, if you substitute the back into the second log you'll get it to be undefined (you get the log of a negative number). The 'solution' is not within the intersection of the domains of the two logs. As a result there is no solution in the real number set to this equation, as evident from plotting the two curves.
https://www.desmos.com/calculator/uuoxq7iiro


That is of course assuming that the equals sign should be a negative.

[Bluegirl]

Just hold up a min, if you substitute the back into the second log you'll get it to be undefined (you get the log of a negative number). The 'solution' is not within the intersection of the domains of the two logs. As a result there is no solution in the real number set to this equation, as evident from plotting the two curves.
https://www.desmos.com/calculator/uuoxq7iiro
(Image removed from quote.)

That is of course assuming that the equals sign should be a negative.

Is actually a plus haha. Failure on my part

[Stick]

Thanks!

Now for
ln(3x-2) = ln(x=1)

Was I right in making it ln(3x-2/x=1)
What do I do now?

Either that way, or just equate what's in the brackets.

[rhinwarr]

I feel so dumb. I didn't even think of that D: I blame the equals sign haha

[Rod]

How do I find the inverse of a 3x3 matrix?

[scribble]

you do it on a cas.
you will never be asked to find the inverse of a 3x3 matrix by hand in vce. save that for linear algebra in uni

[Rod]

you do it on a cas.
you will never be asked to find the inverse of a 3x3 matrix by hand in vce. save that for linear algebra in uni

Thank you

[M-D]

I've got a question from the Maths Quest 11 Mathematical Methods CAS textbook. I have attached my own working out as well as the relevant pages from the textbook.

Thanks in advance for your help

[ealam2]

Dilation away from the x-axis is the same as saying 'dilation in the y direction' or 'parallel to y-axis' since it's going away from the x-axis and going closer to y

[Tasmania Jones]

There's a way to find the inverse (of a 3x3 matrix) by hand but it's incredibly annoying and time-consuming. 

[Einstein]

already upto chapter 2? :O

We have our chapter 1 SAC this Thursday lol

[alchemy]

If g(x) = x^3+2 and f(x)=sqrt(x+3) then what is the largest possible range of g for f[g(x)] to be defined?

[IndefatigableLover]

How would I go about finding the implied domain for ?

EDIT: LOL awks the actual question was but I've worked it out using the examples from below!

[Zealous]

How would I go about finding the implied domain for ?

Let the denominator equal 0 then solve for x. The denominator of a fraction cannot be 0 as anything divided by 0 is undefined.





(You can solve this by using hybrid functions, or simply by using symmetry)

Therefore the domain is all real numbers excluding plus or minus 3/2.

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