Question

solve the equation for x: logx+log(x+2)=log(3x)
A.) there is no solutions
B.) x=1
C.) x=0
D.) x=0,1

Answer 1

log(x)+log(x+2)=log(3x)
log(x(x+2))=log(3x)
=>
x(x+2)=3x (if x>0)
Solve for x.

Answer 2

logx+log(x+2)=log(3x)

1. Simplify logx+log(x+2) to logx(x+2)
logx(x+2)=log3x

2. Cancel log on both sides
x(x+2)=3x

3. Expand
x^2+2x=3x

4. Move all terms to one side
x^2+2x−3x=0

5. Simplify x^2+2x−3x to x2−x
x^2−x=0

6. Factor out the common term x
x(x−1)

7. Solve for x
(Ask yourself, When will x(x−1) equal zero?)

Answer 3

i think its when you have to equal x=o and x-1=0 so that it would be -1 or am i wrong?

Answer 4

is the answer D?

Answer 5

@samsan9
Recall that you have log(3x) on the right hand side, and the domain of log(x) is x>0.
So when you solve the quadratic, be sure to reject all x<0 or x=0.

Answer 6

so it would mean that x=1 since it seems like you are telling me that x shouldn't equal zero

Answer 7

Yes, I AM.
Recall I put "if x>0" to take care of this situation.

Answer 8

so it is B?

Answer 9

Yes @samsan9

Answer 10

thanks you too :)