Hi! Could someone possibly help me solve this?; log2(x+4)=log2(x^2+2). For my answer, I got "All Real Numbers" or x=0 but I'm not sure if that's right. Thanks a bunch!
if course not "all reals" plug in just some value and see whether the equation balances. In particular, try x=0:
log(4) =?= log(2)
I don't think so.
What you need to realize is that if
2^x = 2^y
or
log2(x) = log2(y)
or
2x = 2y
or
2+x = 2+y
or in general, for any function, if
f(x) = f(y)
then x=y. So, we have
log2(x+4) = log2(x^2+2)
so,
x+4 = x^2+2
x^2-x-2 = 0
(x-2)(x+1) = 0
x = 2 or -1
You can see that in either case,
x+4 = x^2+2