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Home » Jari has \(\frac54\) gallons left. - Tacotoon

Jari has \(\frac54\) gallons left. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Using the property \( \log_b(a) + \log_b(c) = \log_b(ac) \),

📌 \[ \log_2(8x) = 5 \].

📌 Rewrite 8 as \( 2^3 \), so \( \log_2(8x) = \log_2(2^3 \cdot x) = \log_2(8x) \).

📌 Thus, \( 2^5 = 8x \).

📌 Solving \( 32 = 8x \), divide by 8, \( x = 4 \).

📌 A triangle has sides of length 7, 24, and 25. Determine if it is a right triangle.

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

📌 Check: \( 7^2 + 24^2 = 49 + 576 = 625 \).

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Solve for \(x\): \(\log_2(x^2 - 5x) = 3\).
Rewrite: \(x^2 - 5x = 2^3 = 8\).
So, \(x^2 - 5x - 8 = 0\).
Use quadratic formula: \(x = \frac{5 \pm \sqrt{25 + 32}}{2}\).
\(x = \frac{5 \pm \sqrt{57}}{2}\).
Approximately, \(x \approx 6.27\) or \(x \approx -1.27\).
Only \(x \approx 6.27\) is valid since \(x^2 - 5x > 0\).
#### 6.27Question: Let $ x, y, z $ be positive real numbers such that...
Solution: To minimize the expression
S = \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x},

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