1700 Followers Problem

Algebra Level 3

{x36x2+5x=02x411x3+23x299x+45=0\begin{cases} x^3-6x^2+5x=0 \\ 2x^4-11x^3+23x^2-99x+45=0 \end{cases}

If AA satisfy the root that satisfy the system of equations above? What is the value of 1700logA1717logA17001700^{\log_{A}17}-17^{\log_A1700} ?

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