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# C3 help!! watch

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i understand:
if e^x = 3........... Then X = ln 3

But when its:

(2e^ 4x) - 3 = 8

What happens to the 2 in front of the e.

I thought: 2 (4x) - ln3 = ln 8 .... but don't think thats right.

2nd.

How to find the inverse. I understand for simple function...but when its
F(x) = (2e^2x+4), for all real numbers.

3. domain is the measure of the x value.

and 4. do you have to learn all the trig identities or are some given in the formula sheet.

Thank you very much.Kam.
2. (Original post by kam_007)

i understand:
if e^x = 3........... Then X = ln 3

But when its:

(2e^ 4x) - 3 = 8

What happens to the 2 in front of the e.

I thought: 2 (4x) - ln3 = ln 8 .... but don't think thats right.
2nd. Is that suppose to be or

3rd. Are you trying to find the domain?

4. It's a good idea to learn them
3. ok... here's the solution

(2e^4x)-3= 8 must be treated like any other algebraic problem as in you have to isolate the term containing x first.

So, first you add 3 on both sides so as to eliminate it from the left hand side (LHS)

now you have 2e^4x=11

divide both sides by 2 and you get e^4x= 11/2

now, ln both sides and you get 4x= ln (11/2)
therefore x = 1/4 ln (11/2) which can also be written as x= ln(11/2)^(1/4)

hope that cleared your doubt (or did i confuse you more??? :P)
4. (Original post by whizkid)
ok... here's the solution

(2e^4x)-3= 8 must be treated like any other algebraic problem as in you have to isolate the term containing x first.

So, first you add 3 on both sides so as to eliminate it from the left hand side (LHS)

now you have 2e^4x=11

divide both sides by 2 and you get e^4x= 11/2

now, ln both sides and you get 4x= ln (11/2)
therefore x = 1/4 ln (11/2) which can also be written as x= ln(11/2)^(1/4)

hope that cleared your doubt (or did i confuse you more??? :P)
Duhhhhhhhhhhhhhhh

I feel like such a pillock!!

You just get rid of the front term.......Thanks alot damn im dumb.
5. ANy thoughts about the inverse function one...??!
6. Lol... i've had a whole year's worth of practice. You are not dumb! I found it pretty confusing when i started as well!!
7. 2. Long time since I done C3 now

Spoiler:
Show

So try to get x on its own and then that is your inverse function after you replace the x with and you replace all y's with x's.

8. Thanks a bunch got it.... but how do you work out the domain. isit the range of the orginal function?
9. ok... for inverses, you know that you have to replace x with y and vice versa right??

So, let F(X) be y
therefore, your problem is now, y= (2e^2x+4)
now, you replace x with y and y with x

so, now you have, x= (2e^2y+4)

1/2 x = (e^2y+4)

ln (1/2 x) =2y+4
so, 2y = ln(1/2 x)-4
y= 1/2 ln (1/2 x)-2

so, y= (ln (1/2 x)^1/2 ) -2
10. (Original post by kam_007)
Thanks a bunch got it.... but how do you work out the domain. isit the range of the orginal function?
yes usually
11. Thanks got it......

Got a fractions question:

(x + (1/x) - 2) / (x - 1)......simplify??

12. I'll edit this but its just clearer for me to see.

Ok:

time the whole thing by x/x:

Now it depends which way you want to do this. You can do algebraic long division or you can do that A, B, C method (forgotten the name).

13. I believe the answer is x-1
14. (Original post by boy)

I believe the answer is x-1
You've multiplied the top by x but not the bottom

If something factorises, factorise it
15. (Original post by boy)

I believe the answer is x-1
I get it.....

but you would have to times top and bottom by x...which would give you x-1 / x

x^2 - 2x + 1 / x^2 - x

(x - 1) (x - 1) / x (x-1)

x - 1 / x
16. (Original post by sohanshah)

I'll edit this but its just clearer for me to see.

Ok:

time the whole thing by x/x:

Now it depends which way you want to do this. You can do algebraic long division or you can do that A, B, C method (forgotten the name).
How'd you guys get the umber cool..... real letters, to make it so clear.
17. Sorry, my mistake
18. You mean Latex.

Put everything in [ latex ] tags

http://www.thestudentroom.co.uk/wiki/LaTex
19. (Original post by kam_007)
How'd you guys get the umber cool..... real letters, to make it so clear.
It's called latex.

Use  tags and put the maths in the middle.

Here's the guide to it.
20. Can anyone explain range and domain to me. Its now the one thing im getting stuck on......

Also do you have to learn all the trigonometric identities?

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