Not Quite Fibonacci

Let us define a recursive relation of MnM_n as follows:

{M1=1M2=2Mn=Mn1Mn2 for n>2\begin{cases} M_1 = 1 \\ M_2 = 2 \\ M_n = M_{n-1} M_{n-2}\text{ for }n>2 \end{cases}

What is log2(M17)\log_2({M_{17}})?

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