SOLUTION: solve the following equation log3 (x+4)+log3 (x-2)=3

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

RELATED QUESTIONS
Solve the logarithmic equation for x. log3 4 + log3 x = log3 6 + log3(x −... (answered by stanbon,nakaguma)

log3(x-2)+log3(x+4)=3 (answered by nerdybill)

solve:... (answered by nerdybill)

solve log3(x-3) + log3(x+2) = log3... (answered by rothauserc)

solve 2 log3)=log3) (4)+ log3)... (answered by Alan3354)

solve the following logarithmic equation. Exact answers only. log3(x+4)=2+log3(x-20) (answered by Alan3354)

Solve the equation exactly for x: log3... (answered by Fombitz)

Solve the following equation for x. Log3 (5x + 4 ) = 6 (answered by josgarithmetic)

solve the equation. log3(x+2)= -2 (answered by edjones)