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Questions about solving equations with indices

I somewhat have trouble with getting all indices on one side
so the question is

3/4x to the power of 3 - 6/x = 0

So i took the 6/x to the other side, but now with the powers wouldnt I take the 6/x and multiply x3 by the x on that side to get x4? the answer book gets x down to the power of 3 but I dont know how
Reply 1
Can you use brackets to make it clear what you mean 3/4x^3 could mean quite a few things.
Reply 2
Original post by SunDun111
...


As above, could you provide a picture or make use of brackets to clarify your meaning. What you've written could mean (34x)3\left(\frac{3}{4x}\right)^3, it could mean 3/4x33/4 \cdot x^3 it could mean 34x3\frac{3}{4x^3}, etc...
Reply 3
Original post by Zacken
As above, could you provide a picture or make use of brackets to clarify your meaning. What you've written could mean (34x)3\left(\frac{3}{4x}\right)^3, it could mean 3/4x33/4 \cdot x^3 it could mean 34x3\frac{3}{4x^3}, etc...


Its 3/4 as a number then x3 next to it, basically 0.75x to the power of 3
Reply 4
Original post by SunDun111
Its 3/4 as a number then x3 next to it, basically 0.75x to the power of 3


Okay, so 3x346x=0\frac{3x^3}{4} - \frac{6}{x} = 0. First step, as you said, bring the 6/x6/x to the other side, this gets us: 3x34=6x\frac{3x^3}{4} = \frac{6}{x}.

Multiply both sides by xx:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}\frac{3x^4}{4} = 6\end{equation*}

.

Divide both sides by 34\frac{3}{4}:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}x^4 = 6 \times \frac{4}{3} = 8\end{equation*}

.

Take the fourth root of both sides, see if you can do this yourself:

Spoiler



Which step don't you understand?
(edited 7 years ago)
Reply 5
Original post by Zacken
Okay, so 3x346x=0\frac{3x^3}{4} - \frac{6}{x} = 0. First step, as you said, bring the 6/x6/x to the other side, this gets us: 3x34=6x\frac{3x^3}{4} = \frac{6}{x}.

Multiply both sides by xx:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}\frac{3x^4}{4} = 6\end{equation*}

.

Divide both sides by 34\frac{3}{4}:

Unparseable latex formula:

\displaystyle [br]\begin{equation*}x^4 = 6 \times \frac{4}{3} = 8\end{equation*}

.

Take the fourth root of both sides, see if you can do this yourself:

Spoiler


Which step don't you understand?


Nothing thanks, I knew how to do it and I got what you got but I realised I wasnt getting the right answer because i copied down the wrong equation
Reply 6
Original post by SunDun111
Nothing thanks, I knew how to do it and I got what you got but I realised I wasnt getting the right answer because i copied down the wrong equation


Ouch, that's good then - you know your understanding and methodology is correct. Well done!
Reply 7
Original post by Zacken
Ouch, that's good then - you know your understanding and methodology is correct. Well done!

Thanks, quick question when you differentiate something and asked to prove its a decreasing function what do you do?
Reply 8
Original post by SunDun111
Thanks, quick question when you differentiate something and asked to prove its a decreasing function what do you do?


Remember yesterday I told you that to show a function is increasing, you show it's derivative is always positive? Can you guess what you have to do for decreasing functions?

Spoiler

Reply 9
Original post by Zacken
Remember yesterday I told you that to show a function is increasing, you show it's derivative is always positive? Can you guess what you have to do for decreasing functions?

Spoiler



too much revision I forget things haha thanks
Reply 10
Original post by SunDun111
too much revision I forget things haha thanks


Don't worry about it, it's good that you're asking and clearing things up. You're welcome.
Reply 11
Original post by Zacken
Don't worry about it, it's good that you're asking and clearing things up. You're welcome.


I looks at your posts on Domains and Range's and for some reason I simply struggle to understand it, I really need to learn it as in C3 a lot of topics are linked with it, do you recommend any good videos about it? because i really struggle with it
Reply 12
Original post by SunDun111
I looks at your posts on Domains and Range's and for some reason I simply struggle to understand it, I really need to learn it as in C3 a lot of topics are linked with it, do you recommend any good videos about it? because i really struggle with it


Which bits do you struggle to understand?

If I told you to find me the domain of 1x1\frac{1}{x-1} what is your thought process?
Reply 13
Original post by Zacken
Which bits do you struggle to understand?

If I told you to find me the domain of 1x1\frac{1}{x-1} what is your thought process?


I struggle with all of it, in the exercise book the questions are difficult because they ask me to sketch the graph of it which I hate doing because some of the graphs are difficult to draw,
Is it the number for which the calculator displays an error?
Reply 14
Original post by SunDun111
I struggle with all of it, in the exercise book the questions are difficult because they ask me to sketch the graph of it which I hate doing because some of the graphs are difficult to draw,
Is it the number for which the calculator displays an error?


Yes, whenever you're given a fraction function (called a rational function), the domain will be the set of numbers for which the denominator is not zero.

So in this case, the domain is x10    x1x- 1 \neq 0 \iff x \neq 1.

What about the domain of x2\sqrt{x-2}? What do you know about square roots, what does that mean for their domain?

Get used to graph sketching, it's a very important skill.
Reply 15
Original post by Zacken
Yes, whenever you're given a fraction function (called a rational function), the domain will be the set of numbers for which the denominator is not zero.

So in this case, the domain is x10    x1x- 1 \neq 0 \iff x \neq 1.

What about the domain of x2\sqrt{x-2}? What do you know about square roots, what does that mean for their domain?

Get used to graph sketching, it's a very important skill.

Would it be 1 because 1-2 is negative square root?
Reply 16
Original post by SunDun111
Would it be 1 because 1-2 is negative square root?


No, in this case you know that your square root is valid as long as the inside of it is positive or zero, so x20    x2x-2 \geq 0 \iff x \geq 2.

So your domain is x2x \geq 2. Perhaps you should go over this with a teacher? :smile:
Reply 17
Original post by Zacken
No, in this case you know that your square root is valid as long as the inside of it is positive or zero, so x20    x2x-2 \geq 0 \iff x \geq 2.

So your domain is x2x \geq 2. Perhaps you should go over this with a teacher? :smile:


Yeah I'm going to when I'm back at school on the 11th, but its so long I want to learn it now, just looking for a few videos.
Reply 18
Original post by SunDun111
Yeah I'm going to when I'm back at school on the 11th, but its so long I want to learn it now, just looking for a few videos.


Video 1

Video 2

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