Question 475057: Use properties of logarithms to solve the equation log(base3)x + log(base3)(x + 2) = log(base3)2 + log(base3)12
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Use properties of logarithms to solve the equation:
log(base3)x + log(base3)(x + 2) = log(base3)2 + log(base3)12
:
log3(x) + log3(x+2) = log3(2) + log3(12)
:
Adding logs is multiply so we can write it:
log3(x(x+2)) = log3(2*12)
:
log3(x^2+2x) = log3(24)
:
if the logs are equal, the expression are equal so we can write it:
x^2 + 2x = 24
:
x^2 + 2x - 24 = 0
factors to
(x+6)(x-4) = 0
Two solutions
x = -6, not a solution, can't have a log of a neg value
:
x = 4 is our solution
:
:
Check it in the original equation
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