SOLUTION: Log 2 (x-2) + log 2 (x+1) =2

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Question 1082312: Log 2 (x-2) + log 2 (x+1) =2
Found 3 solutions by Alan3354, MathTherapy, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Log 2 (x-2) + log 2 (x+1) =2
----
Log(x-2) + log(x+1) = log(2^2)
For any base.
Can you do the rest?

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Log 2 (x-2) + log 2 (x+1) =2
highlight_green%28matrix%281%2C3%2C+x%2C+%22=%22%2C+3%29%29

Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
log%282%2C%28x-2%29%29 + log%282%2C%28x%2B1%29%29 = 2 ---->

log%282%2C+%28%28x-2%29%2A%28x%2B1%29%29%29 = 2                 (due to the property of logarithms log%28a%2C%28b%29%29 + log%28a%2C%28c%29%29 = log%28a%2C%28b%2Ac%29%29 valid  for any base a>0 and any b>0, c>0)

log%282%2C%28x%5E2-x-2%29%29 = 2  ---->

x%5E2+-+x+-+2 = 2%5E2 = 4  ---->

x%5E2+-+x+-+6 = 0  ---->

Factor left side:

(x+2)*(x-3) = 0.

The roots are x= -2 and x= 3.

Only the root x= 3 survives under logarithms.


Answer.  The only solution is x= 3.

On logarithms, their properties and logarithmic equations see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".