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

Question 1082312: Log 2 (x-2) + log 2 (x+1) =2
Found 3 solutions by Alan3354, MathTherapy, ikleyn:
Answer by Alan3354(69443)   (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)   (Show Source): You can put this solution on YOUR website!

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

Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.

+ = 2 ----> = 2 (due to the property of logarithms + = valid for any base a>0 and any b>0, c>0) = 2 ----> = = 4 ----> = 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".

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