Logarithmic Applications: Evaluating Real-Life Scenarios

A scientist measures the pH level of a solution, which is given by the formula pH = -log[H+]. If the concentration of hydrogen ions [H+] is 0.001 M, what is the pH level?

• 4

• 5

• 3

• 2

A sound engineer records the intensity of sound in decibels using the formula dB = 10 * log(I/I0), where I0 is the reference intensity. If the intensity of a sound is 0.0001 W/m², what is the sound level in decibels?

• 30 dB

• 70 dB

• 100 dB

• 50 dB

A population of bacteria doubles every hour. If the initial population is 100, how many hours will it take for the population to reach 800? Use the logarithmic function to find your answer.

• 2 hours

• 3 hours

• 4 hours

• 5 hours

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake has a magnitude of 5.0, how many times more intense is it than an earthquake with a magnitude of 3.0?

• 100

• 200

• 10

• 50

A bank offers an interest rate of 5% compounded annually. If you invest $1000, how long will it take for your investment to double? Use the formula A = P(1 + r)^t and solve for t using logarithms.

• 12.5 years

• 10 years

• 14.21 years

• 20 years

A light source emits light intensity that decreases with distance according to the formula I = I0 / d². If the initial intensity is 1000 lumens and the distance is 10 meters, what is the intensity at that distance?

• 0.1 lumens

• 10 lumens

• 1 lumen

• 100 lumens

A cell phone plan charges $30 per month plus $0.10 per minute of calls. If you want to keep your bill under $50, how many minutes can you talk? Set up an inequality and solve using logarithms.

• 199

• 150

• 250

• 300

A tree grows at a rate proportional to its current height. If a tree is currently 2 meters tall and grows to 8 meters in 3 years, what is the growth rate? Use logarithmic functions to find the answer.

• 0.4624

• 0.2500

• 0.5789

• 0.3215

A recipe calls for a specific ratio of ingredients that can be represented by a logarithmic function. If the ratio of sugar to flour is given by log(sugar/flour) = 0.5, what is the ratio of sugar to flour?

• 4:1

• 3.162:1

• 1:2

• 2:1