Logarithmic Applications: Evaluate & Convert Log Expressions

A scientist measures the pH level of a solution and finds it to be 3. What is the hydrogen ion concentration in moles per liter? (Use the formula pH = -log[H+])

• 0.01 moles per liter

• 0.001 moles per liter

• 0.0001 moles per liter

• 0.1 moles per liter

The population of a bacteria culture doubles every 3 hours. If the initial population is 500, how long will it take for the population to reach 8000? (Use the formula N = N0 * 2^(t/T))

• 12 hours

• 6 hours

• 15 hours

• 24 hours

A sound intensity level is measured at 80 dB. What is the intensity of the sound in watts per square meter? (Use the formula L = 10 log(I/I0) where I0 = 10^-12 W/m²)

• 0.0001 W/m²

• 0.1 W/m²

• 0.01 W/m²

• 0.001 W/m²

A car's value depreciates according to the formula V = V0 * e^(-kt). If the initial value of the car is $20,000 and k = 0.15, what will the value be after 5 years?

• 9448

• 7500

• 15000

• 12000

The half-life of a radioactive substance is 10 years. If you start with 100 grams, how much will remain after 30 years? (Use the formula A = A0 * (1/2)^(t/T))

• 5 grams

• 12.5 grams

• 25 grams

• 50 grams

If log(x) = 2, what is the value of x? (Convert the logarithmic expression to exponential form)

• 100

• 10

• 50

• 1000

A bank offers an interest rate of 5% compounded annually. If you invest $1000, how much will you have after 10 years? (Use the formula A = P(1 + r/n)^(nt))

• 1500.00

• 1628.89

• 2000.00

• 1200.50

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how many times more intense is it than one that measures 4.0? (Use the formula I = 10^(M1 - M2))

• 100

• 200

• 50

• 10

A certain species of fish grows according to the model P(t) = P0 * e^(rt). If the initial population is 200 and the growth rate is 0.03, what will the population be after 5 years?

• 232

• 300

• 250

• 210

If ln(x) = 3, what is the value of x? (Convert the natural logarithm expression to exponential form)

• e^3

• e^4

• e^2

• ln(3)