Thread: rearranging power and log equations

Hello,

I have two equations that I want to reaarange, one a power, the other a log. I can solve the orignal equations but am getting stuck trying to make x the subject. Any help would be appreciated.

eq. 1: y= 4.3316x0.4671

To solve this (for x=8) I did the following: 4.3316 * 80.4671
= 8^(1/10 000) PWR 4671
= 4.3316 *2.64
= 11.44
I think this is right but don't know how to rearrange to get x= ?

Eq 2. y=9.5818ln(x) - 9.5878
Can solve this ok but stuck on same point - getting x=

Thanks

Eq 2:


Eq 1:
This one is not clear in my opinion.

I assume the problem (1) is to solve for x. (If you don't use LaTeX, at least use "^" to indicate powers.)

Start with the obvious: divide both sides by 4.3316:
and then take the .4671 root of both sides: .

No logarithm need.

If the x had been in the exponent, then you would need the logarithm:

Thanks for both your answers - it's so obvious when someone shows you how!

I also apologise for the rather sloppy nature of the post re. layout etc. Will make sure I'm clear if I need to post again.

Thanks again.

[QUOTE=Siron;675593]Eq 2:


Sorry to be stupid but I can't seem to get a sensible answer drom the above equation that you kindly showed me how to rearrange. When I solve the original equation for y using a series of values for x, I can't then use those same values of y to get the corresponding values of x that I used - I end up with insanely large values for x.

What I would give to be good at maths

I don't get your point, do you understand the steps I did or not? Can you give an example where you're stuck?

And it's not stupid, it's important to ask things what you don't understand.

Ok. Here is my problem. Let's say in the original equation x =49. If I am correct this would give a value for y of 27.7. So now I want to use the rearranged equation, using this value of y (27.7), to get back to the original value of x I used (49) - to check I understand how to do it. This is where I am stuck. Looking at the equation, e is the base, which is ln or 2.718281828. Am I right here? y+9.5878/9.5818 is the power? This produces absurdly large anwers. I'm sure there is something pretty fundamental that I am not understanding?!

It's the same, indeed when then . When we substitutie this value for y in the equation:
then we get:



So the rearranged equation is fully equivalent with the original one.
Does this answer your question?

Yes thanks. Just realised what I've been doing wrong -trying to do the sum in the wrong order, which explains why I was getting it wrong and now it is correct. Thanks again.

You're welcome!