Few HW problems involving Logs, Natural logs, and Continuity.

Hi. I'm having problems with a few HW problems.

1) log5 (x) + log5 (x+4) = ?

How would I solve this? I get as far as log5 x^2+4x, but then I'm lost.

2) (4x^3 - 5x^2 + 8x -7)/ ( x-1) for x<1

-3x^2 +3x + a for x>=1

solve for a.

I can't seem to get rid of the (x-1) successfully

3) e^(x+3) = e^(x) +7

solve for x

This one seems like it should be simple , but I can't solve it past

x^2 +3x = ln7

I don't really need the answers to these. I would just like to know how to solve them. I've been stuck on them for hours.

Thanks