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Solve the equation $$\log_{2010}(2009x) = \log_{2009}(2010x)$$.
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is a fraction. With $$a = \log 2009$$, $$b = \log 2010$$ and $$t = \log x$$, the equation is $$\frac{a + t}{b} = \frac{b + t}{a}$$, i.e. $$a^2 - b^2 = t(b - a)$$. Since $$a \ne b$$, $$t = -(a + b)$$, so $$x = \frac{1}{2009 \times 2010} = \frac{1}{4038090}$$.
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