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lg 4x + lg 2x - 4 = 0

 May 24, 2014

Best Answer 

 #1
avatar+128707 
+5

By a log property we can write

Log 4x + Log 2x = Log (8x^2)       So this gives us

Log(8x^2) - 4 = 0      Subtract 4 from both sides

Log (8x^2) = 4          Which says that, exponentially

10^4 =  8x^2       

10,000 = 8x^2           Divide by 8 on both sides

1250 = x^2                Take the square root of both sides

±√(1250) = x =       ± 25√(2).....we must reject the negative root because it would mean that we would have the log of a negative number in the original equation, and that's undefined.

 May 24, 2014
 #1
avatar+128707 
+5
Best Answer

By a log property we can write

Log 4x + Log 2x = Log (8x^2)       So this gives us

Log(8x^2) - 4 = 0      Subtract 4 from both sides

Log (8x^2) = 4          Which says that, exponentially

10^4 =  8x^2       

10,000 = 8x^2           Divide by 8 on both sides

1250 = x^2                Take the square root of both sides

±√(1250) = x =       ± 25√(2).....we must reject the negative root because it would mean that we would have the log of a negative number in the original equation, and that's undefined.

CPhill May 24, 2014

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