How do I solve this log equation via algebra?

You started out right, but you have to continue solving for x after.

log (x + 4) - log (x) = log (x + 2)

log ((x + 4)/x) = log (x + 2)

(x + 4)/x = x + 2

Multiply both sides by x.

x + 4 = x^2 +2x

Subtract x and 4 from both sides.

x^2 + x - 4 = 0

Quadratic formula.

[-b +or- root(b^2 - 4ac)] /2

[-1 +or- root(1 - -16)] / 2

[-1 +or- root(17)] / 2

You can remove the "minus" option because if you did it that way, x would be negative, and that goes against log domains.

So, your answer is:

[-1 + root(17)] / 2

hope i helped :)

well if its just log of base 10 then u just get rid of all the logs so itll be (x+4)/x=x+2.

(x+4)/x = x+2 --->x+4 = x^2 + 2x --->x^2+x-4 = 0 -->x = (-1 + sqrt17)/2