Question 238613: I am struggling to solve this problem:
3 to the square root of 12x + 3 3 to the square root of 3x
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4
Sorry I don't know how to formally write it out on the computer Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! [3 (raised to the power of the radical 12x) +3 ] all divided by 4 is equal to 3 (raised to the power of the radical 3x),
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[3^(sqrt(12x)) + 3]/4 = 3^(sqrt(3x))
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Multiply both sides by 4; Also simplify sqrt(12x) = 2sqrt(3x)
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[3^[2sqrt(3x)]+3] = 4*3^(sqrt(3x))
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[3^sqrt(3x)]^2 + 3 = 4*3^(sqrt(3x))
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This is a quadratic where the variable is 3^(sqrt(3x))
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Let m = 3^(sqrt(3x))
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Substitute to get the following quadratic:
m^2 - 4m + 3 = 0
Factor and solve for "m":
(m-3)(m-1) = 0
m = 3 or m = 1
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Convert back to "x":
3^(sqrt(3x))= 3
sqrt(3x) = 1
3x = 1
x = 1/3
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OR
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3^(sqrt(3x)) = 1
sqrt(3x) must be 0
3x = 0
x = 0
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Final answer: x = 1/3 or x = 0
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Cheers,
Stan H.
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