Logarithmic Applications: Evaluating & Solving in Real Life

1. 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 of the solution?

• 1

• 7

• 10

• 3

2. The population of a certain bacteria doubles every 3 hours. If the initial population is 500, how long will it take for the population to reach 8000? Use logarithms to solve the exponential equation.

• 12 hours

• 15 hours

• 10 hours

• 6 hours

3. A sound intensity level is measured in decibels (dB) using the formula L = 10 log(I/I0), where I is the intensity of the sound and I0 is the reference intensity (1 x 10^-12 W/m²). If a sound has an intensity of 1 x 10^-10 W/m², what is its sound level in decibels?

• 10 dB

• 20 dB

• 30 dB

• 50 dB

4. An investment of $1000 grows at an annual interest rate of 5%, compounded annually. How many years will it take for the investment to grow to $2000? Use logarithms to solve the exponential equation.

• 12.75

• 14.21

• 10.5

• 16.3

5. The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake has a magnitude of 6.5, what is the intensity of the earthquake compared to a reference intensity of 1.0?

• 10000.00

• 500.00

• 50.00

• 316227.77

6. A car's value depreciates at a rate of 15% per year. If the car is currently worth $20,000, how many years will it take for the car's value to drop below $10,000? Use logarithms to find the answer.

• 10

• 3

• 7

• 5

7. The half-life of a radioactive substance is 5 years. If you start with 80 grams of the substance, how much will remain after 15 years? Use logarithmic expressions to solve the problem.

• 5 grams

• 20 grams

• 40 grams

• 10 grams

8. A certain type of bacteria grows according to the model P(t) = P0 * e^(kt). If the initial population is 200 and the growth constant k is 0.3, what will the population be after 4 hours? Use logarithms to evaluate the expression.

• 500

• 600

• 664

• 800

9. The formula for the amount of time it takes for an investment to double is given by the rule of 72: t = 72/r, where r is the interest rate. If you want to double your money in 6 years, what interest rate do you need?

• 12

• 8

• 10

• 6

10. A photographer uses a camera with a lens that has a focal length of 50 mm. The exposure time is determined by the formula t = 2^(-f/10), where f is the f-stop number. If the f-stop number is set to 4, what is the exposure time? Use logarithms to solve the equation.

• 1.000

• 0.757

• 0.300

• 0.500