Solve for x and v and then check the domain of log.
In the answers, it says these two don't have any solutions. I don't understand how, though.
log(v-2) = 1 +log(v+2)
and
2 + logx = log(x-9)
For the first one, I did:
log(v-2/v+2) = 1
v-2/v+2 = 10
v-2 = 10v + 20
0 = 9v + 22
So I didn't get no solution. I don't know if this is right, though.
For the second one, I did:
2 = log(x-9) - logx
2 = log(x-9/x)
100 = x-9/x
100x = x-9
99x = -9
Same thing with this one.
Your workings are fine. However, it is correct that there are no solutions because of the domain restrictions.
is only valid for [/tex]a>0[/tex]
In your first equation
In your second equation
If you check your solution against the domain restriction you'll find the values are not in the domain so there are no solutions