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📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Express 16 as a power of 2: \( 16 = 2^4 \), so \( 16^{x-1} = (2^4)^{x-1} = 2^{4(x-1)} \).

📌 Equation becomes: \( 2^{x+1} = 2^{4x - 4} \).

📌 Equate exponents: \( x + 1 = 4x - 4 \).

📌 Solve: \( 1 + 4 = 4x - x \rightarrow 5 = 3x \rightarrow x = \frac{5}{3} \).

📌 #### \(\frac{5}{3}\)

📌 A ladder 13 meters long leans against a wall, with its base 5 meters from the wall. How high up the wall does the ladder reach?

📌 Use the Pythagorean theorem: \( a^2 + b^2 = c^2 \).

📌 Let \( a = 5 \) (base), \( c = 13 \) (ladder), solve for \( b \) (height).

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