SOLUTION: These problems have me stumped, any help would be greatly appreciated! 1. solve for x: (x-3)/2 - 3|2x-1|=-5/3 2. solve for x: log(base 3)(x+3)-log(base3)(x-1)=2

Question 492747: These problems have me stumped, any help would be greatly appreciated!
1. solve for x: (x-3)/2 - 3|2x-1|=-5/3
2. solve for x: log(base 3)(x+3)-log(base3)(x-1)=2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. solve for x: (x-3)/2 - 3|2x-1|=-5/3
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|2x-1| = 2x-1 if x >= 1/2
|2x-1| is 1-2x if x < 1/2
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Consider x< 1/2 to get:
(x-3)/2 -3(1-2x) = -5/3
x-3 - 6(1-2x) = -10/3
x-3-6+12x = -10/3
13x = -10/3+9 = 17/3
x = 17/39
But 17/39 is not less than 1/2 so no solution in the interval x < 1/2
------------------------
Consider x >= 1/2
(x-3)/2 - 3(2x-1) = -5/3
---
Multiply thru by 6:
3(x-3) - 18(2x-1) = -10
3x-9 -36x+18 = -10
-33x = -19
x = 19/33 which is > 1/2
---
That is the solution.
===============================

2. solve for x: log(base 3)(x+3)-log(base3)(x-1)=2
---
log3[x+3)/(x-1)] = 2
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(x+3)/(x-1) = 9
---
x+3 = 9x-9
8x = 12
x = 3/2
===================
Cheers,
Stan H.

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