Log(x+10)-log(x+4)=logx

how do you solve this?

log(x+10)-log(x+4)=logx
x(x + 4) = x + 10
x^2 + 3x - 10 = 0
(x + 5)(x - 2) = 0
x = -5 , 2 => reject -5
x = 2

Regards.

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subtracting logs can be combined into a division
log[(x+10)/(x+4)] = log x
raise by 10 power
10^log etc.
10^log cancels out, left with
(x+10)/(x+4) = x
subtract x
(x+10)/(x+4) - x = 0
plugging this in calc: x = -5 and 2