You can check your answers to any "solving" problem by plugging them back into the original problem. In your case:
. . . . .x = 1:
. . . . .log(3 + 3) - 2log(4) ?=? 2log(3)
. . . . .log(6) - log(16) ?=? log(9)
. . . . .log(6/16) ?=? log(9)
. . . . .log(3/8) ?=? log(9)
Since 3/8 does not equal 9, your solution is unlikely to be correct. On the other hand:
. . . . .x = 2/3:
. . . . .log(2 + 3) - 2log(2/3 + 1) ?=? 2log(3)
. . . . .log(5) - 2log(5/3) ?=? log(9)
. . . . .log(5) - log(25/9) ?=? log(9)
. . . . .log((5/1)/(25/9)) ?=? log(9)
. . . . .log(9) ?=? log(9)
So the book's solution is correct.
Without seeing your work, it is difficult to suggest where you may have made an error.
Eliz.
Edit: Please post any follow-ups to your
other posting of this exercise.