Hey guys, I'm having trouble with a couple of grade 12 math questions. A friend of mine told me about this forum, and spoke highly of the positive response to all of his posts. I have been attempting these questions for so long but I can't seem to find a solution. These question are homework material. I know the answers (well if the back of the book is correct) but i need to understand the concepts behind the work.

These are my questions:

1. log a (x+2) + log a (x-1) = log a (8-2x)

**Attempt:**
***Well we know that when log a M = log a N then M = N***

Since the base of the log's are the same we can drop the log a

According to product exponent law we know that: (a^x) (a^y) = (a^x+y)

(x+2) (x-1) = (8-2x)

x^2 -x +2x - 2 - 8 + 2x = 0

Mr F says: Therefore x^2 + 3x - 10 = 0 => (x + 5)(x - 2) = 0 .... One of these solutions is invalid ..... (why?)
???????????????????

2. log 5 (x-1) + log 5 (x-2) - log 5 (x+6) = 0

**Attempt:**
Since the base of the log's are the same we can drop the log 5

According to product exponent law we know that: (a^x) (a^y) = (a^x+y)

According to quotient exponent law we know that: (a^x)/(a^y) = (a^x-y)

( (x-1) (x+2) / (x+6) ) = 0

Mr F says: Therefore .

Therefore (x - 1)(x + 2) = x + 6. Now expand the left hand side and simplify the equation into the form quadratic = 0. Then solve the quadratic for x. You only want solutions that satisfy the original equation.
???????????????????