Solve log4 x + log4(x-2)=log4(15)

Question

I know how do the example in my book but I don't know what I'm doing wrong here.

log4 x + log4(x-2)=log4(15)
log4 [x + log4(x-2)]=log4(15)
(x^2 + x)=4
x^2 + x-4=0

Answer 1

I see two major errors

1. from log A + log B = log (A x B)
your second line should have been
log4 [x(x-2)]=log4(15)

then in your third line

the right side should have been 15, not 4

so

x(x-2) = 15
x^2 - 2x - 15 = 0
(x-5)(x+2) = 0
x = 5 or x = -2, but x+-2 does not work since you cannot take the log of a negative

so x=5

Answer 2

should have been
x-5)(x+3) = 0
x = 5 or x = -3, but x=-3 does not work since you cannot take the log of a negative

so x =l 5 is still the only solution