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Solving Exponential & Log Equations with Logarithms — Easy Worksheet 1
Grade 11 · MathSheets Name: ____________________ Date: __________
Solve for x. Round to the nearest hundredth unless the answer is a whole number.
How to solve
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Example
Solve: 6x = 168
Answer: x = 2.86
Not quite. The answer is
💡 Take ln of both sides: ln(2x) = ln(7). Power rule: x·ln(2) = ln(7), so x = ln(7) ÷ ln(2). On a calculator: x ≈ 1.9459 ÷ 0.6931 ≈ 2.8074. Rounded to the nearest hundredth, x = 2.81.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(2x) = ln(7). Power rule: x·ln(2) = ln(7), so x = ln(7) ÷ ln(2). On a calculator: x ≈ 1.9459 ÷ 0.6931 ≈ 2.8074. Rounded to the nearest hundredth, x = 2.81.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 2x = 178
✓ 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
💡 Take ln of both sides: ln(4x) = ln(125). Power rule: x·ln(4) = ln(125), so x = ln(125) ÷ ln(4). On a calculator: x ≈ 4.8283 ÷ 1.3863 ≈ 3.4829. Rounded to the nearest hundredth, x = 3.48.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(4x) = ln(125). Power rule: x·ln(4) = ln(125), so x = ln(125) ÷ ln(4). On a calculator: x ≈ 4.8283 ÷ 1.3863 ≈ 3.4829. Rounded to the nearest hundredth, x = 3.48.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 3x = 102
✓ 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
💡 Divide both sides by 4 to isolate the power: 5x = 236 ÷ 4 = 59. Take ln of both sides and use the power rule: x·ln(5) = ln(59), so x = ln(59) ÷ ln(5). On a calculator: x ≈ 4.0775 ÷ 1.6094 ≈ 2.5335. Rounded to the nearest hundredth, x = 2.53.
✓ Correct!
Not quite. The answer is
💡 Divide both sides by 4 to isolate the power: 5x = 236 ÷ 4 = 59. Take ln of both sides and use the power rule: x·ln(5) = ln(59), so x = ln(59) ÷ ln(5). On a calculator: x ≈ 4.0775 ÷ 1.6094 ≈ 2.5335. Rounded to the nearest hundredth, x = 2.53.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 3x = 91
✓ 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
💡 Take ln of both sides: ln(2x) = ln(146). Power rule: x·ln(2) = ln(146), so x = ln(146) ÷ ln(2). On a calculator: x ≈ 4.9836 ÷ 0.6931 ≈ 7.1898. Rounded to the nearest hundredth, x = 7.19.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(2x) = ln(146). Power rule: x·ln(2) = ln(146), so x = ln(146) ÷ ln(2). On a calculator: x ≈ 4.9836 ÷ 0.6931 ≈ 7.1898. Rounded to the nearest hundredth, x = 7.19.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 3x = 89
✓ 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
💡 Take ln of both sides: ln(2x) = ln(156). Power rule: x·ln(2) = ln(156), so x = ln(156) ÷ ln(2). On a calculator: x ≈ 5.0499 ÷ 0.6931 ≈ 7.2854. Rounded to the nearest hundredth, x = 7.29.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(2x) = ln(156). Power rule: x·ln(2) = ln(156), so x = ln(156) ÷ ln(2). On a calculator: x ≈ 5.0499 ÷ 0.6931 ≈ 7.2854. Rounded to the nearest hundredth, x = 7.29.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 6x = 177
✓ 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
💡 Take ln of both sides: ln(6x) = ln(154). Power rule: x·ln(6) = ln(154), so x = ln(154) ÷ ln(6). On a calculator: x ≈ 5.0370 ÷ 1.7918 ≈ 2.8112. Rounded to the nearest hundredth, x = 2.81.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(6x) = ln(154). Power rule: x·ln(6) = ln(154), so x = ln(154) ÷ ln(6). On a calculator: x ≈ 5.0370 ÷ 1.7918 ≈ 2.8112. Rounded to the nearest hundredth, x = 2.81.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 2x = 51
✓ 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
💡 Divide both sides by 9 to isolate the power: 2x = 171 ÷ 9 = 19. Take ln of both sides and use the power rule: x·ln(2) = ln(19), so x = ln(19) ÷ ln(2). On a calculator: x ≈ 2.9444 ÷ 0.6931 ≈ 4.2479. Rounded to the nearest hundredth, x = 4.25.
✓ Correct!
Not quite. The answer is
💡 Divide both sides by 9 to isolate the power: 2x = 171 ÷ 9 = 19. Take ln of both sides and use the power rule: x·ln(2) = ln(19), so x = ln(19) ÷ ln(2). On a calculator: x ≈ 2.9444 ÷ 0.6931 ≈ 4.2479. Rounded to the nearest hundredth, x = 4.25.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 4x = 157
✓ 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
💡 Take ln of both sides: ln(6x) = ln(136). Power rule: x·ln(6) = ln(136), so x = ln(136) ÷ ln(6). On a calculator: x ≈ 4.9127 ÷ 1.7918 ≈ 2.7418. Rounded to the nearest hundredth, x = 2.74.
✓ Correct!
Not quite. The answer is
💡 Take ln of both sides: ln(6x) = ln(136). Power rule: x·ln(6) = ln(136), so x = ln(136) ÷ ln(6). On a calculator: x ≈ 4.9127 ÷ 1.7918 ≈ 2.7418. Rounded to the nearest hundredth, x = 2.74.
💡 How to solve: Solving Exponential & Log Equations with Logarithms
Isolate the exponential part, then take ln (or log) of both sides and use the power rule to bring the exponent down: ax = N gives x = ln(N) ÷ ln(a). For log equations, combine the logs into one, rewrite in exponential form, and reject any solution that makes the inside of a log zero or negative.
Try a similar one
Solve: 7x = 181
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Solving Exponential & Log Equations with Logarithms — Easy Worksheet 1
Solve for x. Round to the nearest hundredth unless the answer is a whole number.