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Properties of Logarithms — Easy Worksheet 1
Grade 11 · Whoobee Name: ____________________ Date: __________
Use the properties of logarithms.
How to solve
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Example
Fill in the blank: log2(16m) = ___ + log2(m)
Answer: 4
Not quite. The answer is
💡 Quotient rule: log5(y125) = log5(y) − log5(125). Then log5(125) = 3, because 53 = 125. The blank is 3.
✓ Correct!
Not quite. The answer is
💡 Quotient rule: log5(y125) = log5(y) − log5(125). Then log5(125) = 3, because 53 = 125. The blank is 3.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log2(4x) = ___ + log2(x)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Product rule: log4(2) + log4(8) = log4(2 × 8) = log4(16). Rewrite: log4(16) = x means 4x = 16, and 4 × 4 = 16, so x = 2. The answer is 2.
✓ Correct!
Not quite. The answer is
💡 Product rule: log4(2) + log4(8) = log4(2 × 8) = log4(16). Rewrite: log4(16) = x means 4x = 16, and 4 × 4 = 16, so x = 2. The answer is 2.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log3(27m) = ___ + log3(m)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Quotient rule: log5(175) − log5(7) = log5(175 ÷ 7) = log5(25). Since 5 × 5 = 25, log5(25) = 2. The answer is 2.
✓ Correct!
Not quite. The answer is
💡 Quotient rule: log5(175) − log5(7) = log5(175 ÷ 7) = log5(25). Since 5 × 5 = 25, log5(25) = 2. The answer is 2.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log2(y2) = log2(y) - ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Power rule: the exponent comes down in front of the log, so log5(x8) = 8 · log5(x). The blank is 8.
✓ Correct!
Not quite. The answer is
💡 Power rule: the exponent comes down in front of the log, so log5(x8) = 8 · log5(x). The blank is 8.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log3(9m) = ___ + log3(m)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 First find the log: 2 × 2 = 4, so log2(4) = 2. Then multiply: 3 × 2 = 6. The answer is 6.
✓ Correct!
Not quite. The answer is
💡 First find the log: 2 × 2 = 4, so log2(4) = 2. Then multiply: 3 × 2 = 6. The answer is 6.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log3(y3) = log3(y) - ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Product rule: log(2) + log(50) = log(2 × 50) = log(100). log with no base means base 10. Rewrite: log(100) = x means 10x = 100, and 10 × 10 = 100, so x = 2. The answer is 2.
✓ Correct!
Not quite. The answer is
💡 Product rule: log(2) + log(50) = log(2 × 50) = log(100). log with no base means base 10. Rewrite: log(100) = x means 10x = 100, and 10 × 10 = 100, so x = 2. The answer is 2.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log5(y7) = ___ · log5(y)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Quotient rule: log3(21) − log3(7) = log3(21 ÷ 7) = log3(3). Since 31 = 3, log3(3) = 1. The answer is 1.
✓ Correct!
Not quite. The answer is
💡 Quotient rule: log3(21) − log3(7) = log3(21 ÷ 7) = log3(3). Since 31 = 3, log3(3) = 1. The answer is 1.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log5(5y) = ___ + log5(y)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Power rule: the exponent comes down in front of the log, so log3(m9) = 9 · log3(m). The blank is 9.
✓ Correct!
Not quite. The answer is
💡 Power rule: the exponent comes down in front of the log, so log3(m9) = 9 · log3(m). The blank is 9.
💡 How to solve: Properties of Logarithms
Product rule: logb(MN) = logb(M) + logb(N). Quotient rule: logb(M/N) = logb(M) - logb(N). Power rule: logb(Mk) = k·logb(M). Combine or split the logs, then use logb(bk) = k.
Try a similar one
Fill in the blank: log5(y3) = ___ · log5(y)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Properties of Logarithms — Easy Worksheet 1
Use the properties of logarithms.