ALPHA DIVISION

Question 54

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Question

Let

\begin{aligned} f(x)={}&\log_8x\log_{16}x\log_{128}x+\log_4x\log_{16}x\log_{128}x\\ &+\log_4x\log_8x\log_{128}x+\log_4x\log_8x\log_{16}x, \end{aligned}

and

g(x)=\log_4(x^2)\log_8(x^2)\log_{16}(x^2)\log_{128}(x^2)

. How many real

x

satisfy

f(x)=g(x)

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