Logarithms... (1 Viewer)

[Cleft]

NEW QUESTION!

This question is taken from Maths in Focus 2.

a) Use Simpson's Rule with three function values to find the area bounded by the curve y = ln x, the x-axis and the lines x = 2 and x = 4.
b) Change the sucject of y = ln x to x.
c) Hence find the exact area in part (a)

Okay, so I'm fine in part's (a) and (b), but (c) really has me stuck. Can anyone help?

 

[lyounamu]

2^(x+1) = 10^2x

HELP!

x+1 = log2(10^2x)
x+1 = 2x log2(10)
x+1-2x(log2(10)) = 0
x(1-2(log2(10)) +1 = 0
x = -1/(1-2(log2(10))

 

[clintmyster]

log₁₀2^{x + 1} = log₁₀10^2x
(x + 1)log₁₀2 = 2x log₁₀10
(x+1)/2x = Log₁₀10/Log₁₀2

theres some rearranging here:

x = 1/ (2xLog₁₀10/Log₁₀2 -1)
x = 0.1771838201

and daym u namu!

 

[lyounamu]

log₁₀2^{x + 1} = log₁₀10^2x

???

 

[clintmyster]

I was just checking if it was coming out the right way with the whole sup and sub thingy

 

[Cleft]

Thanks everyone, new question now though.

 

[lyounamu]

NEW QUESTION!

This question is taken from Maths in Focus 2.

a) Use Simpson's Rule with three function values to find the area bounded by the curve y = ln x, the x-axis and the lines x = 2 and x = 4.
b) Change the sucject of y = ln x to x.
c) Hence find the exact area in part (a)

Okay, so I'm fine in part's (a) and (b), but (c) really has me stuck. Can anyone help?

y = ln x.

x = e^y

When x = 2, y = ln2
When x = 4, y = ln4

Integrate e^y and the terminals are ln2 and ln4.

So [e^y] (ln4 -> ln2)
Area = e^(ln4) - e^(ln2) = 2

 

[Cleft]

Oh, so I just had to sub the x-values into the equations?
Gawd... I feel so stupid now.
Haha, and to think, my friend doing 4-Unit Mathematics couldn't even figure it out...

 

[lyounamu]

Oh, so I just had to sub the x-values into the equations?
Gawd... I feel so stupid now.
Haha, and to think, my friend doing 4-Unit Mathematics couldn't even figure it out...

If you change your subject, you will have to change the terminals too in respect to that value.

 

[Cleft]

Haha, yeah that makes sense.
I guess just seeing it as something different freaked me out.

Thankyou once again =D

 

[Cleft]

Sorry for the double posting...
But the answer in my book gives 2.16...
Eeep.

 

[Timothy.Siu]

NEW QUESTION!

This question is taken from Maths in Focus 2.

a) Use Simpson's Rule with three function values to find the area bounded by the curve y = ln x, the x-axis and the lines x = 2 and x = 4.
b) Change the sucject of y = ln x to x.
c) Hence find the exact area in part (a)

Okay, so I'm fine in part's (a) and (b), but (c) really has me stuck. Can anyone help?

e^y=x
so
integral of e^y from ln4 to ln 2=2
integral of e^y from ln 2 to 0 =1 2ln2-1= the area from 2 to 1
4ln4 is the area of the box
so 4ln4 - 2 - 1 - (ln4-1) is the area
umm
i got 2.16
its a hard question.

 

[Cleft]

Hmmm, I'm just trying to figure out what you're reffering to.
So you're making a complete box from zero to ln4 across to x=4, then removing the unneeded parts?

 

[Timothy.Siu]

Hmmm, I'm just trying to figure out what you're reffering to.
So you're making a complete box from zero to ln4 across to x=4, then removing the unneeded parts?

yeah basically, just draw it out
but if u change the subject, and u find the area and subtract it from the box, u still need to remove the area from 1 to 2 since the question is asking you to find it from 2 to 4