SOLUTION: Hi, I need help in solving this logarith problem:- Solve the simultaneous equations log(x+y)= 2log(x) (this equation doesn't have any base) log(y)= log(2)+ log(x-1) My

Question 486725: Hi, I need help in solving this logarith problem:-
Solve the simultaneous equations
log(x+y)= 2log(x) (this equation doesn't have any base)
log(y)= log(2)+ log(x-1)
My attempt:
I simplified the first line :-
log(x+y)= 2log(x)
=log(x,x+y)= log(x,x^2) (I put the (x) as a base)
=log(x,x+y)= 2 (I simplified log(x,x^2) to number 2)
= x^2= x+y
Similarly I simplified the second line to be (y = 2x-2)
I don't know what to do any further now.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Your work so far is good!
1) and...
2) Substitute this for y in equaton 1) to get...
1a) Simplify and solve for x:
1b) Solve by factoring:
1c) so...
1d) or Now plug each of these, in turn, in equation 2 and solve for y.
2a) Substitute :
2b) and...
2c) Substitute :
2d)
So there are four possible solutions:
(1, 0), (1, 2), (2, 0), (2, 2)
Let's check them all:
Substitute and

This solution is valid!
Try the other solutions yourself and see what happens!
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