SOLUTION: find the value(s) of x if 2log3x = log3 (x+6)

Question 584722: find the value(s) of x if 2log3x = log3 (x+6)
Answer by Schaman_Dempster(26) (Show Source): You can put this solution on YOUR website!
2log3x = log3 (x+6)
Using the property of logarithm such that n log a = log a^n
log3 x^2 = log3 (x+6)
Since the logs on both the sides have same bases, they can be canceled out.
So, x^2 = x + 6
x^2 - x - 6 =0
Now, factoring by regrouping:

x^2 - 3x + 2x -6 = 0
x(x -3) + 2(x-3) = 0
(x-3) (x +2) = 0
x = 3 , x =-2
Since originally we had the term 2 log3 x..which shows that x should always be greater than 0 {Because log of negative number is not defined}
Thus, x = 3
Hope this helps~!
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