VCE Methods Question Thread!

[MoonChild1234]

Solve the equation log5(x) = 16logx(5)

Given that q^p=25, find log5(q) in terms of p

I was just stuck on these two questions, how do I solve for the variable?

[Tau]

Solve the equation log5(x) = 16logx(5)

I was just stuck on these two questions, how do I solve for the variable?

The trick here is to use the change of base law \(\log_b(a)=\frac{\log_c a}{\log_c b}\) to obtain everything in the same base. Note that I've just used \(\log\) without specifying any base as the specific base is irrelevant.

\begin{align}
\log_5(x) &= 16\log_x(5) \\
\dfrac{\log x}{\log 5} &= 16\left(\dfrac{\log5}{\log x} \right)\\
(\log x)^2 &= 16(\log5)^2\\
\log x&=\pm 4\log 5\\
\log x&=\log 5^{4},\log 5^{-4}\\
x&= 5^{4},5^{-4}
\end{align}

Given that q^p=25, find log5(q) in terms of p

Solve for q in terms of p, then substitute that into the given expression.
\begin{align}
q^p=25 &\implies q=25^{1/p}\\
&\implies \log_5(q)=\log_5(25^{1/p})=\frac{1}{p}\log_5(25)=\frac{2}{p}

\end{align}

[jashaan]

Hi!

Could someone please help me with 6c?

Thanks!

[Sine]

Hi!

Could someone please help me with 6c?

Thanks!

I wont fully solve the question but will be happy to give you a couple of hints

Split up the first integral into two integrals.

Also note: int(f(x)) from 2 to 4 + int (f(x)) from 4 to 5 = int(f(x)) from 2 to 5

[FrankieDens]

Hi everyone!

I just have a general question on how to use Checkpoints. There's a specific chapter for Extended response questions (like Exam 2 type questions) and I was wondering if I should do these throughout the year or once I've finished content to ensure I'm familiar with my CAS calculator?

Thanks~ 

[Tau]

Hi everyone!

I just have a general question on how to use Checkpoints. There's a specific chapter for Extended response questions (like Exam 2 type questions) and I was wondering if I should do these throughout the year or once I've finished content to ensure I'm familiar with my CAS calculator?

Thanks~ 

I’d recommend doing them throughout the year. Especially before SAC’s, I’d go through and complete the relevant extended response questions for the assessable content.

[colline]

Hi everyone!

I just have a general question on how to use Checkpoints. There's a specific chapter for Extended response questions (like Exam 2 type questions) and I was wondering if I should do these throughout the year or once I've finished content to ensure I'm familiar with my CAS calculator?

Thanks~ 

Adding on to what Tau said, you definitely do not want to leave it to after you finish all content when you’re juggling exam revision with four other subjects as well, not to mention solving application problems is a skill you must build up gradually over the year.

[jashaan]

Hi!
I am really confused about as to why the answer is positive 1/root 2 for question m. I understand why it is 1/root 2 however I get confused when it comes to the positive/negative symbols.

Thank you

[Sine]

Hi!
I am really confused about as to why the answer is positive 1/root 2 for question m. I understand why it is 1/root 2 however I get confused when it comes to the positive/negative symbols.

Thank you

Now picture the unit circle and "count" backwards i.e. clockwise on the unit circle from 0. Being by going backwards to -3pi which is the same positive as -pi and (pi). Then rotate clockwise another pi/4.

You end up in the 2nd quadrant where sine is positive thus you get the positive solution

[M-D]

Hi

Could some please help me factorise the following

Question:
Answer:

I have tried using the different of perfect square rule for the start of it but I can't get an answer which matches the solutions.

Thanks

[colline]

Hi

Could some please help me factorise the following

Question:
Answer:

I have tried using the different of perfect square rule for the start of it but I can't get an answer which matches the solutions.

Thanks

Here's my working out. You can also do it without substituting (a+b) and (a-b) but I just thought it makes it clearer.

[IThinkIFailed]

Hey, I don’t know if I’ve antiderived this expression properly

3/(4x^2)
= 12x^-2
= -12x^-1
=-12/x
=-3/4x

I feel I can’t exactly do what I did in the last step

[MB_]

Hey, I don’t know if I’ve antiderived this expression properly

3/(4x^2)
= 12x^-2
= -12x^-1
=-12/x
=-3/4x

I feel I can’t exactly do what I did in the last step

Your second step doesn't work
\[\begin{align*}f'(x) &=\frac{3}{4x^2}\\ &=\frac{3x^{-2}}{4}\\ f(x) &=\frac{3x^{-1}}{-4}\\ &=\frac{-3}{4x}\end{align*}\]

[IThinkIFailed]

Your second step doesn't work
\[\begin{align*}f'(x) &=\frac{3}{4x^2}\\ &=\frac{3x^{-2}}{4}\\ f(x) &=\frac{3x^{-1}}{-4}\\ &=\frac{-3}{4x}\end{align*}\]

Thank you so much!

This seems like a really simple question, but how do I go about solving this?

e^x=3

I have a inkling I have to convert to natural log, but I don’t know what do after i do this:
loge(x)=loge(3)

[sk2000]

This seems like a really simple question, but how do I go about solving this?

e^x=3

I have a inkling I have to convert to natural log, but I don’t know what do after i do this:
loge(x)=loge(3)

No need for the two natural logs, simply create a log keeping e as the base and 3 as the number. Keep in mind that you're solving for x, so x must be on its own on one side. This becomes x = loge(3)