Question 303588: Solve this equation:
(log base6 x)^2 - 3*(log base 6 x) - 2 = 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (log base6 x)^2 - 3*(log base 6 x) - 2 = 0
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Let log6(x) = w
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Substitute to get:
w^2 - 3w -2 = 0
Solve for "w":
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w = [3 +- sqrt(9 -4*-2)]/2
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w = [3 +- sqrt(17)]/2
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w = (3+sqrt(17))/2 or w = (3-sqrt(17))/2
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Substitute to solve for "x":
log6(x) = {3+sqrt(17)]/2 or log6(x) = (3-sqrt(17))/2
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x = 6^(3.5616) or x = 6^(-0.5616)
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x = 2.7351 or x = 0.3656
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Cheers,
Stan H.
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