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I have a couples problems with certain types of problems. I cant seem how to figure these ones out, any help is appreciated.
1. Find x and express answer in terms of natural logarithms: 2e^3x=6
2. Express 1+ ln as a single logarithm.
3. Write log(x+3) in terms of natural logarithms.
4. Solve with Gauss Jordan method (I can get half way done but I never seem to be able to finish the whole problem.)
x-y-3z=2
2x-y-4z=3
x+y-z=1
5. How to Maximize Z=2x-3y subject to
2x+y>=1
x-y=<1
x,y>=0
6. Similar can probably figure it with some help from previous one.
Maximize Z=2x-3y subject to
-x+y=<2
3x+y=<18
x,y>=0
All help appreciated.
I'll try #4.)
x-y-3z=2
2x-y-4z=3
x+y-z=1
r means row
r1: 1 -1 -3 2 (r3-r1)/2 0 1 1 -.5 3(r1-r2) 0 0 1 -3/6
r2: 2 -1 -4 3 (2/3)(r3-.5r2) 0 1 2/3 -1/3 copy r2-> 0 1 2/3 -1/3
r3: 1 1 -1 1 copy r3 ---> 1 1 -1 1 copy r3-->1 1 -1 1
exchange rows 3 and 1:
r1: 1 1 -1 1
r2: 0 1 2/3 -1/3
r3: 0 0 1 -3/6
Try to make it
1 0 0
0 1 0
0 0 1, that's what we will try now....
new row1 will be r1 - r2 + (5/3)r3 ---> 1 0 (-5/3 + 5/3) (1 + 1/3 - 5/6)
new row2 will be r2 - (2/3)r3 -----> 0 1 (2/3 - 2/3) (-1/3 + (2/3)(3/6))
row 3 is already done: 0 0 1 -3/6 or -.5
We did it, made a diagonal of 1's, the rest is zeros except for answer column on right, the 4th column.
column 1, row 1 is x, which equals right column, row 1: (1 + 1/3 - 5/6) or 1 + 2/6 - 5/6 or 1/2 is x.
column 2, row 2 is y, which is 4th column middle row: (-1/3 + (2/3)(3/6)) or zero is y.
column 3, row 3 is z, which is 4th column bottom row: -.5 is z.
So x = .5, y = 0, z = -.5
I hope that helps, I just learned this for the second time in a year from web pages; I hope it's right!!
igloo myrtilles fourmis
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1. Find x and express answer in terms of natural logarithms: 2e^3x=6
2. Express 1+ ln as a single logarithm.
ehm? ln of what?
3. Write log(x+3) in terms of natural logarithms.
im assuming log base 10 since its not specified
in general
The Beginning Of All Things To End.
The End Of All Things To Come.
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2. Express 1+ln as a single logaritm.
I think it's
IPBLE: Increasing Performance By Lowering Expectations.
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