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The inequality $$\log_{a} f(x)<\log_{a} g(x)$$ implies that
f(x) > g(x) > 0 for 0 < a < 1 and g(x) > f(x) > 0 for a > 1
g(x) > f(x) > 0 for 0 < a < 1 and f(x) > g(x) > 0 for a > 1
f(x) > g(x) > 0 for a > 0
g(x) > f(x) > 0 for a > 0
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