SOLUTION: I need help solving this logarithmic equation: log(x-1)+log(x+2)=2

Question 145525: I need help solving this logarithmic equation:
log(x-1)+log(x+2)=2
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Combine the logs using the identity

Foil

Rewrite the equation using the property: ====>

Square 10 to get 100

Subtract 100 from both sides

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

or Break up the expression.

So the possible answers are or

However, since you cannot take the log of a negative number, this means that the only answer is

-------------------------------
Answer:

So our answer is which approximates to

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log(x-1)+log(x+2)=2
log[x^2+x-2] = 2
x^2+x-2 = 10^2
x^2+x-102 = 0
------
x = [-1 +- sqrt(1-4*1*-102)]/2
x = [-1 +- sqrt(409)]/2
x = [-1 +- 20.22]2
Positive solution:
x = 9.612
==========================
Cheers,
Stan H.[
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