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#1 2006-06-19 16:36:16

daniel4544
Guest

Logarithm troubles, Need help quick!

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.dunno

#2 2006-06-20 02:03:51

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Logarithm troubles, Need help quick!

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!!


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#3 2006-06-20 03:25:07

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Logarithm troubles, Need help quick!

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


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The End Of All Things To Come.

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#4 2006-07-22 21:23:41

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Logarithm troubles, Need help quick!

2. Express 1+ln as a single logaritm.

I think it's



so


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