Quick question (1 Viewer)

[kevinexcs]

Got equation

y=e^ 2x or y=e^x
how do you make x the subject?
thanks

 

[tooheyz]

i have no idea... but use logs?
i havent done logs yet, but im just taking a wild guess here. which topic is this?

 

[SoFTuaRiaL]

y = e^2x
ln y = ln (e^2x)
ln y = 2x
x = (ln y)/2

 

[tooheyz]

aah.. there u go! i knew it had something to do with log!

yeah take log of both sides and yeah... (gosh... i remember doing log back in year 10... i hated it!)

 

[SoFTuaRiaL]

Originally posted by ToOhEyZ
aah.. there u go! i knew it had something to do with log!

yeah take log of both sides and yeah... (gosh... i remember doing log back in year 10... i hated it!)

umm tooheyz, ure not 100% right and thats something u gotta be very careful abt in maths ...
u dont take log on both sides, u take ln which is different .... log is generally to the base 10, wheras ln is to the base e ....

 

[tooheyz]

ah same thing to me... i've always hated logs and i never got them

hmm.. and logs r in the 2u syllabus.. AAaaaAHhhHH!!

 

[kevinexcs]

thanks da monsta
didn't expect an answer that quick =D
got a 3unit test soon on logs exp and trig
funny how we are doing 2unit topics in the 3unit exam

 

[Rahul]

we had logs and exp in our 3u test a week ago.....it was not easy
watch out for a curve sketching question with logs and exp

 

[kevinexcs]

Another question further on from the question before
Use the simpson rule with 5 function values to find the volume of the solid formed when the curve y=e^x is rotated about the y-axis from y=3 to y=5.
Answer is 12units^3
And another
y=INx change subject to x

 

[SoFTuaRiaL]

Originally posted by kevinexcs
Another question further on from the question before
Use the simpson rule with 5 function values to find the volume of the solid formed when the curve y=e^x is rotated about the y-axis from y=3 to y=5.
Answer is 12units^3
And another
y=INx change subject to x

will get answer to simpson's rule later ... i'm in uni

y = ln x
e^y = e^ln x
e^y = x

TADAA !!

 

[kevinexcs]

knew i was right =D
oh and dw about the other q
stupid me too much studying i guess and no rest
thanks
i'll be back with 4unit q next time =D

 

[kevinexcs]

sorry another q
a) area bounded by y=inx,the x-axis and the lines x=2,4
using simpson rule.
b)Change subject of y=inx to x
c)Hence find exact area in part a)
Don't need to do (a) and (b) just (c)
well heres what i did
ans for a)2.16
b)x=e^y
c)Interration of e^y dy= [e^y] values are from In4 to In2
I got an answer of 2 from that though the answer in the book says 2.16
what am i doing wrong?

 

[SoFTuaRiaL]

i'm not too sure abt simpson's rule (ask homer ) .... but lets see
u got the answer to part (a) as 2.16 rite? but in part (b) u learn to write y=lnx as x=e^y ... and part (C) says "find the exact answer". since u havent learnt integration by parts in 2u maths, try convert y=ln x into x=e^y and then integrate to find the area ....
but again, i'm not 100% sure if it'd work ...... if i get a proper answer, i'll post it here ...

 

[elizabethy]

Originally posted by kevinexcs
Got equation

y=e^ 2x or y=e^x
how do you make x the subject?
thanks

making x the subject u get,for y=e^x
x=lny

for y=e^2x
x=0.5lny

hope this helps!!

 

[Huy]

Originally posted by kevinexcs
sorry another q
a) area bounded by y=inx,the x-axis and the lines x=2,4
using simpson rule.
b)Change subject of y=inx to x
c)Hence find exact area in part a)
Don't need to do (a) and (b) just (c)
well heres what i did
ans for a)2.16
b)x=e^y
c)Interration of e^y dy= [e^y] values are from In4 to In2
I got an answer of 2 from that though the answer in the book says 2.16
what am i doing wrong?

just a refresh,
simpsons rule: h/3[y0 + yn + 4(y1+y3+...) +2(y2+y4+...)]

where h = b - a / n (number of strips)

you'd have to draw up a table of values for simpsons rule to work out the y values and sub back into simpsons.

b has already been answered,

but it's the same thing as below:

y=e^2x
logeY=logee.2x
logeY=2x
x=logeY/2

y=e^x
logeY=logee.x; [logee = 1]
x=logeY

for c, by drawing the graph of y=logx, x=2 and x=4 shouldnt be a problem since it's above the x-axis

can i get the full question?
because this thread is all over the place,
im not sure what question you're looking for, or what info was given before the q's?

(there was a volume question above i saw, but it doesnt relate to what you're asking?)

but anyway,
'...simpson rule with 5 function values to find the volume of the solid formed when the curve y=e^x is rotated about the y-axis from y=3 to y=5'

recall that V = pi integ. from a to b of x^2 dy
-rotating about the y-axis

so V = pi integ. from 3 to 5 of x^2 dy

then using y = e^x
logeY = logee.x [logee = 1, e^1=e]
x = logeY
x^2 = (logeY)^2
= 2logeY (2lnx); using logaB^c = c.logaB

V = pi integ. from 3 to 5 of 2lnx
taking out 2
= 2.pi [lnx] 3 to 5
= 2.pi {loge5 - loge3}
= 2.pi [loge(5/3)]; recall logeA - logeB = loge(A/B)
= 3.2096...

somehow or other, it seems wrong
i had a 3u test today, didn't really include logs
but had mostly euler's (e^x, exponentials)

i'd like to know the full question though hehe

just on another note,
'a) area bounded by y=inx,the x-axis and the lines x=2,4
using simpson rule.
...
c)Hence find exact area in part a)
...
c)Interration of e^y dy= [e^y] values are from In4 to In2
I got an answer of 2 from that though the answer in the book says 2.16'

using A = integ. f(x) dx -the x-axis,
are you sure you're using y-values, not x values?

your working for c would be 4-2 =2, so i guess that's right.
since e^loge4 - e^loge2 is 4-2 = 2

it's been a while since i've done integ, but that's about all i could figure out, again, could you post the q again (in full? just copy the textbook verbatim) thanks

 

[kevinexcs]

dw about the q
finally did it =/

 

[KeypadSDM]

Originally posted by Da Monstar


umm tooheyz, ure not 100% right and thats something u gotta be very careful abt in maths ...
u dont take log on both sides, u take ln which is different .... log is generally to the base 10, wheras ln is to the base e ....

Actually Log[x] is generally accepted at Log of x to the base e ...
However in 2 unit maths always be pedantic and write Log_e_[x]...

 

[Minai]

Originally posted by KeypadSDM


Actually Log[x] is generally accepted at Log of x to the base e ...
However in 2 unit maths always be pedantic and write Log_e_[x]...

or just write ln(x)
much clearer to the marker which base ur using

 

[woho]

Wow... i'm reviving this thread if nobody minds.....

Having trouble with a Simpson's Rule Question:

"Use Simpson's rule with 3 function values to find the area enclosed by the curve y = e^2x, the y-axis and the line y=3"

Does this mean b= 3 and a = 0?

If so, how can this be possible, as x^2 = (ln y/2)^2- when subbing into simple formula {b-a/6[f(a) + 4((b+a)/2) + f(b)] } f(a) would give ln 0 which is indeterminate

Thanx

 

[SoulSearcher]

Wow... i'm reviving this thread if nobody minds.....

Having trouble with a Simpson's Rule Question:

"Use Simpson's rule with 3 function values to find the area enclosed by the curve y = e^2x, the y-axis and the line y=3"

Does this mean b= 3 and a = 0?

If so, how can this be possible, as x^2 = (ln y/2)^2- when subbing into simple formula {b-a/6[f(a) + 4((b+a)/2) + f(b)] } f(a) would give ln 0 which is indeterminate

Thanx

Think of where the graph y = e^2x cuts the y-axis, that will be your lower limit