VCE Methods Question Thread!

[jazzycab]

Thanks

Also, do you know how to solve 1024 = 2^x without a cas?

Write the left hand side with a base of 2 (i.e. \(1024=2^{10}=2^x\)). Therefore \(x=10\)

[Yertle the Turtle]

Thanks

Also, do you know how to solve 1024 = 2^x without a cas?

You can use logs. 1024=2^x is the same as x=log2(1024).
Personally in this case I would think about the game 2048... lol ;P

[snowisawesome]

Thanks everyone
Am I correct in thinking that 2log_e(2) is the same as log_e(4)
Also, is there a way to work out 2log_e(2) without a cas?

[Sine]

Thanks everyone
Am I correct in thinking that 2log_e(2) is the same as log_e(4)
Also, is there a way to work out 2log_e(2) without a cas?

yes it is the same since the number outside the front can be brought inside as a power.

 2log_e(2)  =  log_e((2)²) = log_e(4)

[Yertle the Turtle]

Thanks everyone
Am I correct in thinking that 2log_e(2) is the same as log_e(4)
Also, is there a way to work out 2log_e(2) without a cas?

Yes, 2log_e(2) is the same as log_e(4) because of your log laws.
I don't think that there is a way to work it out without a CAS.
EDIT: Just beaten by Sine

[snowisawesome]

But i'm doing a cas free question in which 2log_e(2) is the y intercept
So would I just to estimate the value of 2log_e(2)
And also, how would I know if the value of 2log_e(2) is negative or positive?

Thanks again

[Sine]

But i'm doing a cas free question in which 2log_e(2) is the y intercept
So would I just to estimate the value of 2log_e(2)
And also, how would I know if the value of 2log_e(2) is negative or positive?

Thanks again

ln(1) =0
and ln(x) has a positive gradient (i.e. increasing as x increases)
so ln(2) > 0
hence
2ln(2) > 0 hence positive

Usually most would do this quick check subconsciously or in their head but these are the type of thinking you should do.

[jazzycab]

ln(1) =0
and ln(x) has a positive gradient (i.e. increasing as x increases)
so ln(2) > 0
hence
2ln(2) > 0 hence positive

Usually most would do this quick check subconsciously or in their head but these are the type of thinking you should do.

Additionally, because \(e\approx2.718\) we can get a more accurate estimate.

[snowisawesome]

Thanks Sine and Jazzycab
So would both your explanations work in any situation?

Also, does ln(1) mean log(1), and is this the same as log₁₀(1)

[Lear]

In refers to a natural log which means the base is e (2.71828.......) not base 10

[snowisawesome]

In refers to a natural log which means the base is e (2.71828.......) not base 10

Would it be written as log_e(1)?

[Lear]

Indeed

[snowisawesome]

Indeed

Thanks
So if it wasn't about log_e(1) would it usually be written as log₁₀(1)?

[methodsdeficit1011]

Hey guys,

I know this is a stupid question but I keep forgetting the difference between dilations from the x and y axis.
Here's a question that I would appreciate a walkthrough of:

- Find the rule for y = x^3 under the following transformations:
  - a reflection in the y-axis
  - a dilation of factor 3 from the y-axis
  - a translation of 3 units in the positive direction of the x-axis, and 1 unit in + direction of the y-axis

I can visualise it in my head correctly, but usually end up writing the incorrect answer.
So (x,y) --> (-x, y), (-3x, y), (-3x + 3, y +1)
y = -3(x-3)^3 + 1 [I believe this would've been where I messed up]
y = -3(x-3)^3 - 1

Thanks!

[Sine]

Hey guys,

I know this is a stupid question but I keep forgetting the difference between dilations from the x and y axis.
Here's a question that I would appreciate a walkthrough of:

- Find the rule for y = x^3 under the following transformations:
  - a reflection in the y-axis
  - a dilation of factor 3 from the y-axis
  - a translation of 3 units in the positive direction of the x-axis, and 1 unit in + direction of the y-axis

I can visualise it in my head correctly, but usually end up writing the incorrect answer.
So (x,y) --> (-x, y), (-3x, y), (-3x + 3, y +1)
y = -3(x-3)^3 + 1 [I believe this would've been where I messed up]
y = -3(x-3)^3 - 1

Thanks!

- Find the rule for y = x^3 under the following transformations:
  - a reflection in the y-axis
  - a dilation of factor 3 from the y-axis
  - a translation of 3 units in the positive direction of the x-axis, and 1 unit in + direction of the y-axis