Logarithm Word Problems
Solve real-world problems involving logarithms, including exponential growth, decay, and Richter scale calculations.
Includes
Standards
Logarithm Word Problems - Grade 12
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Read each problem carefully and solve for the unknown. Show all your work. Round your answers to two decimal places where appropriate.
1. The population of a certain bacteria doubles every 3 hours. If there are initially 100 bacteria, how long will it take for the population to reach 10,000 bacteria?
2. A radioactive substance has a half-life of 15 years. If a sample initially contains 500 grams of the substance, how many years will it take for the sample to decay to 50 grams?
3. The Richter magnitude (M) of an earthquake is related to the energy (E) released by the formula log₁₀E = 11.8 + 1.5M. How many times more energy is released by an earthquake with a magnitude of 8 compared to an earthquake with a magnitude of 6?
31.62 times
100 times
1000 times
3162.28 times
4. The loudness of a sound (L) in decibels is given by the formula L = 10 log₁₀(I/I₀), where I is the intensity of the sound and I₀ is the reference intensity. If a sound has an intensity of 10⁻⁵ W/m² and the reference intensity is 10⁻¹² W/m², the loudness of the sound is decibels.
5. A solution with a pH of 3 is 100 times more acidic than a solution with a pH of 5.
True
False