Logarithmic Word Problems and Percentages in Real Life

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?

• 10

• 1

• 7

• 3

A sound engineer records a sound that is 90 decibels. If the sound intensity is increased by 10 decibels, what is the new intensity level in terms of logarithmic scale?

• 110 decibels

• 100 decibels

• 80 decibels

• 95 decibels

A population of bacteria doubles every hour. If there are initially 100 bacteria, how many hours will it take for the population to reach 800? Use logarithms to find your answer.

• 5 hours

• 3 hours

• 4 hours

• 2 hours

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 logarithms to solve the problem.

• 20 years

• 5 years

• Approximately 14.2 years

• 10 years

A recipe calls for 2 cups of sugar, which is 25% of the total ingredients. How many cups of ingredients are needed in total? Use percentages to find the answer and express it in logarithmic terms.

• log(6)

• log(4)

• log(8)

• log(10)

A radio station broadcasts at a frequency of 100 MHz. If the frequency is increased to 200 MHz, what is the logarithmic increase in frequency?

• 0.6021

• 0.3010

• 0.2000

• 0.4771

A tree grows at a rate that can be modeled by the equation h(t) = 10 log(t + 1), where h is the height in meters and t is the time in years. What will be the height of the tree after 5 years?

• 5.000 meters

• 7.781 meters

• 15.500 meters

• 10.000 meters

A student scores 85% on a test, which is equivalent to a logarithmic score of log(85). If the student wants to improve their score to 95%, what is the logarithmic increase needed?

• log(10)

• log(85)

• log(95)

• log(95/85)

A city has a population of 1 million people. If the population grows at a rate of 3% per year, how long will it take for the population to reach 2 million? Use logarithms to calculate the time required.

• 23.1 years

• 15 years

• 10 years

• 30 years