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Thus, there are $ \boxed25 $ ways. - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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\( f(2) = 2(4) - 8(2) + 5 = 8 - 16 + 5 = -3 \).
So, the minimum value is \( -3 \).
A geometric sequence has first term 4 and common ratio \( \frac{3}{2}...
Sum of geometric sequence: \( S_n = a \frac{r^n - 1}{r - 1} \),
\( a = 4 \), \( r = \frac{3}{2} \), \( n = 5 \).
\( S_5 = 4 \cdot \frac{(\frac{3}{2})^5 - 1}{\frac{3}{2} - 1} = 4 \cdot...
As fraction: \( \frac{1688}{32} = \frac{211}{4} \).
#### \( \frac{211}{4} \)
Combine logs: \( \log_2(x(x - 2)) = 3 \) → \( x(x - 2) = 2^3 = 8 \).
So, \( x^2 - 2x - 8 = 0 \) → factor: \( (x - 4)(x + 2) = 0 \).

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