You should ALWAYS check your answer by plugging it back into the original equation. In this case, it doesn't fit. I would rather solve your problem this way:
Can you continue from here?
Hi could someone please let me know if this is correct?
Log4_X + log4_(x-3)=1
Log4_X + log4_X - Log4_3=1
Change base ln
Log4_X= lnX/ln4
Log4_3=ln3/ln4
1=lne^1=lne
Now
lnX/ln4 + lnX/ln4 - ln3/ln4 = lne
As all ln the cancel all and solve with algebra
X/4 +X/4 - 3/4 = 1
(2X-3)/4 = 1
2X-3 = 4
2X = 4+3
X = 7/2
Thanks in advance
Neither. The technical explanation is that there is a branch cut discontinuity in the complex plane. That is, you have two surfaces representing the function, and they don't meet on the negative real axis or at zero. It's a lot like a parking garage: you're heading clockwise on one floor, and your friend is heading counter-clockwise on the next floor up. You're not going to meet, are you? That's what this is like.
But that's more than you probably need to know right now. What you need to know right now is that, for real-valued logarithm functions with a positive base, the domain is the positive real numbers. You can't plug zero or a negative number into the logarithm functions you're dealing with.