Question 927887: solve the following equation log3 (x+4)+log3 (x-2)=3
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! log3 (x+4) + log3 (x-2) = 3
us logarithm rule for adding logs with same base
log3 ( (x+4) * (x-2) ) = 3
log3 ( x^2 +2x -8 ) = 3
us definition of logarithm
x^2 +2x -8 = 3^3
x^2 +2x -8 = 27
x^2 +2x -35 = 0
factor polynomial
(x+7)*(x-5) = 0
x = -7 and 5
now the log of a negative number is not defined, therefore
x = 5
check answer
log3 (5+4) + log3 (5-2) = 3
2 + 1 = 3
3 = 3
answer checks
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