Exponentials and Logs help!? (1 Viewer)

[siraulo23]

1) Find the point of intersection of the curves y=logex and y=log10x

2) 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 correct to 3 significant figures

3) Sketch y=log(x-x^2)

Please show working

Thanks in advance!!!

 

[jet]

 

[jet]

 

[siraulo23]

thanks a lot!

question 2 anyone?

 

[ibbi00]

Yo what did you do in the second line to third line?

 

[tommykins]

Should be a ln10.lnx - lnx = 0
lnx(ln10-1) = 0

lnx = 0 thus x = 1.

 

[ibbi00]

Should be a ln10.lnx - lnx = 0
lnx(ln10-1) = 0

lnx = 0 thus x = 1.

That makes more sense

 

[siraulo23]

question 2 lol

 

[tommykins]

question 2 lol

You have the formula, show us your working out or what you've done so far.

 

[tommykins]

Do the maths.

What...?

How does e^2x = 3 turn into 2xe = 3?

 

[ibbi00]

What...?

How does e^2x = 3 turn into 2xe = 3?

Oh wait... Forgot to use ln lol

EDIT: will edit

 

[tommykins]

Oh wait... Forgot to use ln lol

EDIT: will edit

It's also asking for the area with the y axis, not the x.

 

[siraulo23]

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

h=(b-a)/n
h=(3-0)/2 = 3/2

y 0 3/2 3
x (ln0)/2 ln(3/2)/2 (ln3)/2

(ln0)/2= error

 

[tommykins]

h = (3-1)/2 not (3-0)

 

[ibbi00]

 

[siraulo23]

h = (3-1)/2 not (3-0)

this is prolly a dumb question but why? its between y axis and y=3

edit:

 

[ibbi00]

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

h=(b-a)/n
h=(3-0)/2 = 3/2

y 0 3/2 3
x (ln0)/2 ln(3/2)/2 (ln3)/2

(ln0)/2= error

this is prolly a dumb question but why? its between y axis and y=3

also ln(0)/2 = error, or am i doing it incorrectly

Original equation is e^2x ... Therefore, y intercept is 1. You can see that if you set x = 0.

 

[siraulo23]

got it

thank you!!

also, thanks everyone who helped

 

[jet]

Oh sorry about that lol, wasn't concentrating very much.