Question 234053: What are the steps to finding 4(log9 of X)^2 - 2(log9 of X^2)=3?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What are the steps to finding
4(log9 of X)^2 - 2(log9 of X^2)=3?
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It is a quadratic with w = (log9 (x))
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Rewrite as:
4w^2 - 2w - 3 = 0
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w = [2 +- sqrt(4 -4*4*-3)]/8
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w = [2 +- sqrt(52)]/8
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w = [2 +- 2sqrt(13)]/8
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w = [(1/4) + (1/4)sqrt(13)] or w = [(1/4) - (1/4)sqrt(13)]
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Now solve for "x"
log9 (x) = [(1/4) + (1/4)sqrt(13)] or log9 (x) = [(1/4) - (1/4)sqrt(13)]
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x = 9^[(1/4) + (1/4)sqrt(13)] or x = 9^[(1/4) - (1/4)sqrt(13)]
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x = 12.55.. or x = 0.239...
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Cheers,
Stan H.
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