Mastering Logarithmic Conversions and Applications

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

• 1 mole per liter

The population of a bacteria culture doubles every 3 hours. If the initial population is 100, how long will it take for the population to reach 800? (Use logarithmic equations to solve)

• 9 hours

• 15 hours

• 6 hours

• 12 hours

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

• 0.01

• 0.0001

• 0.1

• 0.001

If log base 2 of x is 5, what is the value of x? (Convert the logarithmic form to exponential form)

• 32

• 64

• 16

• 8

A car's value depreciates by 15% each year. If the car is currently worth $20,000, how many years will it take for the value to drop below $10,000? (Use logarithms to find the answer)

• 10

• 5

• 7

• 3

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 properties of logarithms)

• 200

• 100

• 50

• 10

A bank offers an interest rate of 5% compounded annually. If you invest $1,000, how long will it take for your investment to double? (Use the formula A = P(1 + r)^t and convert to logarithmic form)

• Approximately 14.21 years

• 20 years

• 10 years

• 25 years

If log base 10 of y is 2, what is the value of y? (Convert the logarithmic form to exponential form)

• 50

• 100

• 1000

• 10

A certain radioactive substance has a half-life of 5 years. If you start with 80 grams, how much will remain after 15 years? (Use logarithmic properties to solve)

• 5 grams

• 20 grams

• 40 grams

• 10 grams

The decibel level of a sound is given by the formula L = 10 log(I/I0). If the intensity of a sound is 100 times greater than the reference intensity, what is the decibel level? (Apply properties of logarithms to find L)

• 30 decibels

• 20 decibels

• 10 decibels

• 50 decibels