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Worksheet

Logarithm Word Problems

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  1. 1.
    An earthquake of magnitude 66 is compared with one of magnitude 44 on the Richter scale. How many times larger is the amplitude of the stronger earthquake?
    1. a)20
    2. b)1000
    3. c)2
    4. d)100
  2. 2.
    A solution has a hydrogen ion concentration of [H+]=10−5[H^+] = 10^{-5} mol/L. What is its pH?
    1. a)0.000010.00001
    2. b)10510^5
    3. c)−5-5
    4. d)55
  3. 3.
    You invest 1000 dollars at 5%5\% interest compounded once a year. Which expression gives the time tt, in years, until the money doubles?
    1. a)ln⁡2000ln⁡1000\frac{\ln 2000}{\ln 1000}
    2. b)ln⁡2ln⁡0.05\frac{\ln 2}{\ln 0.05}
    3. c)ln⁡2ln⁡1.05\frac{\ln 2}{\ln 1.05}
    4. d)2⋅ln⁡1.052 \cdot \ln 1.05
  4. 4.
    Sound A has a level of 9090 dB and sound B a level of 6060 dB. How many times as intense is sound A as sound B?
    1. a)300
    2. b)1000
    3. c)3
    4. d)30
  5. 5.
    A substance loses 8%8\% of its mass every year. Which equation gives the number of years tt until only half of it remains?
    1. a)t=ln⁡0.5ln⁡1.08t = \frac{\ln 0.5}{\ln 1.08}
    2. b)t=ln⁡0.5ln⁡0.08t = \frac{\ln 0.5}{\ln 0.08}
    3. c)t=0.5⋅ln⁡0.92t = 0.5 \cdot \ln 0.92
    4. d)t=ln⁡0.5ln⁡0.92t = \frac{\ln 0.5}{\ln 0.92}
  6. 6.
    A solution has [H+]=0.001[H^+] = 0.001 mol/L. What is its pH? (The answer is a whole number.)
  7. 7.
    A sound has intensity I=107⋅I0I = 10^7 \cdot I_0. What is its level L=10log⁡(II0)L = 10\log\left(\frac{I}{I_0}\right) in decibels? (The answer is a whole number.)
  8. 8.
    Find the pH of a solution with [H+]=2.5×10−6[H^+] = 2.5 \times 10^{-6} mol/L. Round to two decimal places.
  9. 9.
    An earthquake of magnitude 7.47.4 is compared with one of magnitude 5.65.6. How many times larger is the amplitude of the stronger one? Round to the nearest whole number.
  10. 10.
    A town has 25 00025\,000 inhabitants and grows by 3%3\% per year. After how many years will it reach 40 00040\,000 inhabitants? Round to one decimal place.
  11. 11.
    Lemon juice has a hydrogen ion concentration of [H+]=0.01[H^+] = 0.01 mol/L. Find its pH.
  12. 12.
    A hair dryer produces a sound 1 000 0001\,000\,000 times as intense as the threshold of hearing. Find its level in decibels.
  13. 13.
    A cup of coffee has a pH of 55. Find its hydrogen ion concentration [H+][H^+] in mol/L, written as a decimal number.
  14. 14.
    Heavy traffic measures 8585 dB and a normal conversation 6060 dB. How many times as intense is the traffic noise? Round to the nearest whole number.
  15. 15.
    Money is invested at 6%6\% interest compounded once a year. How many full years does it take until the balance has at least doubled?
  16. 16.
    A lab sample contains 200200 mg of a substance with a half-life of 55 hours. After how many hours will only 2020 mg remain? Round to one decimal place.
  17. 17.
    You invest 3000 dollars at 4%4\% interest compounded continuously, so A=3000e0.04tA = 3000e^{0.04t}. After how many years does the balance reach 4500 dollars? Round to two decimal places.
  18. 18.
    A car bought for 24 00024\,000 dollars loses 15%15\% of its value every year. After how many full years is it first worth less than 60006000 dollars?
Interactive lesson with step-by-step solutions and more practice (free): mathorio.com/en/learn/pre-calculus/logarithms/log-word-problems