Exponents and radicals
Exponential equations without logarithms worksheets
Solve nine types of exponential equations by rewriting to a common base. Choose 12 or 14 questions with exact fraction answers and worked keys.
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Exponential equations requiring logarithms worksheets
Solve six types of exponential equations using logarithms, including natural-base equations. Choose 12, 14 or 16 questions with worked keys and four-place answers.
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Isolate the exponential expression and take logarithms. Keep full calculator precision until the final answer, then round to four decimal places.
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Isolate the power before taking logarithms
Choose six equation forms and 12, 14 or 16 questions. Practice integer bases and the natural base e, with signed linear exponents, outside multipliers and shifts.
The worked key isolates the power, takes logarithms and gives an exact logarithmic expression before the final four-place approximation. Keep calculator precision through every step; round only the answer.
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Learning objective
What this activity builds
Isolate an exponential expression, take logarithms, and solve for the variable before rounding the final answer.
Worked example
Solve 3e^(2x - 1) + 4 = 19.
e^(2x - 1) = 5, so x = (ln(5) + 1) / 2, approximately 1.3047.
Subtract 4, divide by 3, then take the natural logarithm. Since ln(e raised to a power) equals that exponent, the remaining equation is linear.
Teaching notes
Make the practice count
- Remove outside addition and multiplication before taking a logarithm.
- For an integer base b, divide by ln(b) when changing base.
- The symbol e is the natural exponential constant.
- Use the approximation sign for the rounded answer and keep all four decimal places.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose six equation forms and 12, 14 or 16 questions. Take logarithms and round only the final answer to four decimal places.
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Use a calculator to evaluate natural, common and other logarithms. Choose 12, 14 or 16 questions and round answers to two or three decimal places.
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Exponents and radicals
Logarithmic equations worksheets
Solve six types of logarithmic equations with exact answers. Choose 12, 14 or 16 questions and check every solution in the original logarithms.
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