SOLUTION: Solve algebraically. 2log[3](2x)+log[3](3x^(4))=2

Question 282565: Solve algebraically.
2log[3](2x)+log[3](3x^(4))=2
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
Use properties of logs to write expression as a single log.
2log[3](2x)+log[3](3x^(4))= 2
log[3](2x)^2 + log[3](3x^4) = 2
log[3][(2x)^2 * (3x^4)] = 2
Raise base 3 to the number that lies on the other side of the log equation.
3^2 = (2x)^2 * (3x^4)
9 = 12x^6
Take 6th root of both sides.
x = [6throot{48}]/2
Plug this answer for x into the original log equation and simplify to see if the answer is correct.

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