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Exponents and Logarithms · Ages 16–17

Solving Exponential Equations with Logarithms Practice

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Intended for 11th grade math students. Solve each equation using logarithms, giving exact expressions or rounded decimal values.

  1. Solve 2^x = 10 for x, rounded to three decimal places.

  2. Solve 5^(x - 1) = 125 using logarithms.

  3. Solve 3 · 4^x = 48.

  4. Solve e^(0.05t) = 3 for t, rounded to three decimal places.

  5. Solve 7^(2x) = 50 for x, rounded to three decimal places.

  6. Solve 3^(x + 2) = 8^x for x, rounded to three decimal places.

  7. A culture of 200 bacteria doubles every hour according to P(t) = 200 · 2^t. In how many hours will the population reach 5,000? Round to three decimal places.

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Solving Exponential Equations with Logarithms Practice

Answer key

  1. Solve 2^x = 10 for x, rounded to three decimal places.

    x = log(10) / log(2) ≈ 3.322

  2. Solve 5^(x - 1) = 125 using logarithms.

    x = 4

  3. Solve 3 · 4^x = 48.

    x = 2

  4. Solve e^(0.05t) = 3 for t, rounded to three decimal places.

    t = ln(3) / 0.05 ≈ 21.972

  5. Solve 7^(2x) = 50 for x, rounded to three decimal places.

    x = ln(50) / (2 · ln(7)) ≈ 1.005

  6. Solve 3^(x + 2) = 8^x for x, rounded to three decimal places.

    x = (2 · ln(3)) / (ln(8) - ln(3)) ≈ 2.247

  7. A culture of 200 bacteria doubles every hour according to P(t) = 200 · 2^t. In how many hours will the population reach 5,000? Round to three decimal places.

    t = log(25) / log(2) ≈ 4.644 hours