SOLUTION: Hi,I hope someone can answer my log question: log(x+2)-logx= log (x+5) Solve for x. Thanks alot!

Question 4711: Hi,I hope someone can answer my log question:
log(x+2)-logx= log (x+5) Solve for x.
Thanks alot!
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
log(x+2)-logx=(x+5)

Use the second law of logarithms to express the left side as a quotient:

log M = log N means that M=N.
Therefore

Multiply both sides of the equation by x:

Set equal to zero:

Are you sure you copied this right? They "usually" factor at this point. Nevertheless,
Solve by quadratic formula or completing the square. Completing the square is actually easier.
Add +2 to each side and place a blank space on each side of the equation:

Take half of the x coefficient, and square it. Half of 4 is 2, and 2^2 = 4. Add +4 to each side of the equation on the blank lines above:

Take square root of each side of the equation:

Subract 2 from each side:

Of course, you must reject the value , since it makes the log of a negative. The final answer is

Are you sure you didn't copy this wrong??

R^2 at SCC

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