{
  "title": "Common Logarithms (Base 10) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is log₁₀ 100? 🤔", "options": {"A": "1", "B": "2", "C": "10", "D": "100"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Find log₁₀ 1. 😊", "options": {"A": "0", "B": "1", "C": "10", "D": "-1"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "What is log 1000? (Base 10 is implied) 🔢", "options": {"A": "2", "B": "3", "C": "4", "D": "10"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If log₁₀ x = 1, what is x? ✏️", "options": {"A": "1", "B": "10", "C": "0", "D": "100"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Find log 0.1 📉", "options": {"A": "1", "B": "-1", "C": "0", "D": "10"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "What is log₁₀ 10⁵? 🚀", "options": {"A": "5", "B": "10", "C": "50", "D": "10⁵"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If log a = 2, what is a? 🎯", "options": {"A": "20", "B": "100", "C": "2", "D": "200"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Find log 10,000. 🌟", "options": {"A": "3", "B": "4", "C": "5", "D": "10"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "What is log₁₀ √10? 🌱", "options": {"A": "1", "B": "0.5", "C": "2", "D": "10"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If 10³ = 1000, then log 1000 = ? 🔄", "options": {"A": "10", "B": "3", "C": "1000", "D": "1"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Find log 1,000,000. 💎", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "What is log 0.01? ❄️", "options": {"A": "-1", "B": "-2", "C": "2", "D": "0.1"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "If log₁₀ N = 0, then N = ? 🎈", "options": {"A": "0", "B": "1", "C": "10", "D": "100"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Find log (10 × 100). ✖️", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "What is log 10⁻²? 🔽", "options": {"A": "2", "B": "-2", "C": "0.01", "D": "100"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Find log₁₀ (100/10). ➗", "options": {"A": "0", "B": "1", "C": "2", "D": "10"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If log x = -1, then x = ? 🔍", "options": {"A": "1", "B": "0.1", "C": "-10", "D": "10"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "What is log √1000? (approx.) 📏", "options": {"A": "1.5", "B": "3", "C": "2.5", "D": "1"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Find log (10² × 10³). 📚", "options": {"A": "5", "B": "6", "C": "10", "D": "100"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If log₁₀ a = 4, then a = ? 🏁", "options": {"A": "40", "B": "1000", "C": "10,000", "D": "100"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Find log 2 + log 5. (Use log 10 = 1) ➕", "options": {"A": "log 7", "B": "1", "C": "log 25", "D": "2"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Simplify: log 50 - log 5. ➖", "options": {"A": "log 45", "B": "log 10", "C": "1", "D": "2"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "If log 3 ≈ 0.4771, what is log 3000? 🔎", "options": {"A": "3.4771", "B": "4.771", "C": "0.54771", "D": "477.1"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Solve: log x = log 4 + log 25. ⚖️", "options": {"A": "29", "B": "100", "C": "20", "D": "125"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Find log √100 without a calculator. 🌳", "options": {"A": "10", "B": "1", "C": "2", "D": "0.5"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If log (2x) = 1, find x. 🧩", "options": {"A": "2", "B": "5", "C": "10", "D": "20"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Evaluate: log 8 + log 125. (Hint: 8×125=1000) 🧊", "options": {"A": "2", "B": "3", "C": "log 1000", "D": "Both B & C"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "Simplify: log 40 - log 4. 🌀", "options": {"A": "log 36", "B": "1", "C": "log 10", "D": "10"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "If log₁₀ 5 = 0.6990, what is log 500? 📊", "options": {"A": "2.6990", "B": "3.6990", "C": "1.6990", "D": "0.6990"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Solve for x: log x = 2 log 3. ⚡", "options": {"A": "6", "B": "9", "C": "27", "D": "3"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Find log 0.25 if log 2 = 0.3010. 🍕", "options": {"A": "-0.6020", "B": "0.6020", "C": "-0.3010", "D": "0.25"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "What is log (1/100) + log 100? 🤝", "options": {"A": "0", "B": "1", "C": "2", "D": "-1"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If log (x+1) = 1, find x. 🎲", "options": {"A": "9", "B": "10", "C": "11", "D": "0"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Simplify: 2 log 5 + log 4. ✨", "options": {"A": "log 29", "B": "log 100", "C": "2", "D": "log 40"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Find log 250 if log 2 = 0.3010 and log 5 = 0.6990. 🧮", "options": {"A": "1.3980", "B": "2.3979", "C": "1.6990", "D": "2.3010"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Solve: log x = 3 - log 2. 🔢", "options": {"A": "500", "B": "200", "C": "1000", "D": "5"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If log 9 = 2 log 3, find log 27. 📈", "options": {"A": "3 log 3", "B": "log 9 + log 3", "C": "2 log 9", "D": "log 18"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "What is log 6 + log (1/6)? ⚗️", "options": {"A": "log 1", "B": "0", "C": "1", "D": "Both A & B"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "Find the value: log√10 100. 🌿", "options": {"A": "2", "B": "4", "C": "20", "D": "√10"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "If log (x/y) = 0, what can you say about x and y? 🤔", "options": {"A": "x = y", "B": "x = 10y", "C": "y = 10x", "D": "x + y = 10"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Solve for x: log (x-1) + log (x+1) = log 8. 🏆", "options": {"A": "2", "B": "3", "C": "4", "D": "9"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "If log 2 = a and log 3 = b, express log 72 in terms of a and b. 🧬", "options": {"A": "2a + 3b", "B": "3a + 2b", "C": "a² + b³", "D": "6ab"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "Evaluate: (log 5)/(log 2) + (log 8)/(log 5) (approx.). 📉", "options": {"A": "≈ 3.0", "B": "≈ 2.5", "C": "≈ 3.8", "D": "≈ 4.2"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "Prove that 7 log (10/7) + 3 log (21/20) + 2 log (8/3) = log 2. Find its value. ✅", "options": {"A": "0", "B": "1", "C": "2", "D": "log 2"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "If log₁₀ 2 = 0.3010, log₁₀ 3 = 0.4771, find log₁₀ √0.06. 🌌", "options": {"A": "-0.6095", "B": "-1.1095", "C": "0.6095", "D": "1.1095"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "Solve: 2 log x = log 36 - log 4. ⚔️", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Given log 2 = 0.3010, how many digits are in 2¹⁰⁰? 🔢", "options": {"A": "30", "B": "31", "C": "32", "D": "100"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "If log (x² - 4) - log (x-2) = 1, find x. 🎭", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "hard", "question": "Simplify: log (81/80) + 5 log (25/24) + 3 log (8/9). 🌀", "options": {"A": "log 1", "B": "log 2", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "hard", "question": "Find x if logₓ 8 = 0.5. 🧭", "options": {"A": "16", "B": "64", "C": "32", "D": "4"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Given log 5 = 0.6990, find log (0.04)⁻¹. 🔑", "options": {"A": "1.3980", "B": "2.3980", "C": "-1.3980", "D": "0.3010"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "If log (a+b) = log a + log b, find the relation between a and b. 🤯", "options": {"A": "a = b", "B": "a + b = ab", "C": "a = b/(b-1)", "D": "Both B & C"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "Solve: log₂ (log₃ (log₄ x)) = 0. 🏹", "options": {"A": "64", "B": "81", "C": "256", "D": "12"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Evaluate: (1/logₐ bc) + (1/log_b ca) + (1/log_c ab). ♾️", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Find the sum: log (1 + 1/1) + log (1 + 1/2) + log (1 + 1/3) + ... + log (1 + 1/99). ⏳", "options": {"A": "1", "B": "2", "C": "log 100", "D": "log 99!"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "hard", "question": "If x = log 2, y = log 3, express log 2.25 in terms of x and y. 🌳", "options": {"A": "2y - 2x", "B": "2x - y", "C": "y - x", "D": "x + y"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Prove: a^(log b) = b^(log a). If a=10, b=100, what is the value? ⚡", "options": {"A": "10", "B": "100", "C": "1000", "D": "1"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Find x if: log (x+3) - log (x-1) = 1. ✍️", "options": {"A": "2", "B": "7/9", "C": "13/9", "D": "3"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "Given log 2 = 0.3010, find the characteristic of log (0.0025). 📍", "options": {"A": "-2", "B": "-3", "C": "-4", "D": "2"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "If log (a² + b²) = log a + log b + log 2, find a/b + b/a. 🪐", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"}
  ]
}