Logs!
Exponential EQs
Word Problems
More word problems
Solving Log EQ's
100
log (base 2) 8 = ?
What is 3?
100
Write the exponential equation 4^5= 1,024 in logarithmic form.
What is log (base 4) 1,024 = 5 ?
100
If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, how many bacteria will there be in 5 hours? Assume the bacterial growth is modeled by N(t) = 3000e^rt Round to the nearest whole number.
What is 10471 bacteria?
100
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 17e^-0.015t, where m(t) is measured in kilograms. Approximately, how much of the substance will remain after 10 days?
What is m(10)= 14.6 kilograms?
100
Solve: log x = 3
What is 1000?
200
Write the equation log (base 3) 729 = 6 in exponential form.
What is 3^6=729 ?
200
Write the exponential equation 27^ (1/3) = 3 in logarithmic form.
What is log (base 27) 3 = 1/3 ?
200
The population growth of a certain community is modeled by the function P(x) = 500e^0.05x, Where x is in years. Approximately, how long will it take for the population size to reach 200%
What is 14 years
200
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 17e^-0.015t, where m(t) is measured in kilograms. Approximately, how long will it take for the substance to reach 50% of its initial amount?
What is t = 46 days?
200
log (base 3) x = 5
What is x = 243 ?
300
Write the equation log 1000 = 3 in exponential form.
What is 10^3=1000 ?
300
Write the exponential equation (1/2)^-3=8 in logarithmic form.
What is log (base 1/2) 8 = -3
300
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 30,000,000. Round your answer to four decimal places.
What is 7.4771?
300
An investment earning 4.25% interest per year was started in the year 2000. After approximately how many years will the investment reach 300%, if the initial amount invested was $2000. Assume continuous compounded interest.
What 26 years?
300
Solve: 0.5ln x = 4 leave your answer in base e
What is e^8 ?
400
Write log(x - 1) = 2 in exponential form
What is x-1=10^2 ?
400
Is the graph y= .7^x increasing(growth) or decreasing (decay)?
What is decreasing(decay)?
400
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 35,000,000. Round your answer to four decimal places.
What is 7.5441 ?
400
The function N(x) = 500(1.0125)^4x models the amount, B, in an account x years since 1990. How much more money will be in the account after 5 years than it was initially?
What is $141?
400
Solve: (3/2)logx = -1 Round your answer to two decimal places.
What is x= 0.22 ?
500
Write ln(x + 2) = 4 in exponential form
What is x+ 2= e^4
500
ln e ^(3x) = ?
What is 3x?
500
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the intensity of an earthquake with a Richter scale of 7.567 Round to the nearest whole number
What is 36,897,760?
500
A solution’s pH is given by the function p(t) = -log(t), where t is the hydronium ion concentration, in moles per liter. A sample of coffee has a pH of 5.0. What is the approximate hydronium ion concentration of the sample?
What is t = 10^-5 ?
500
Solve: 2/7 log⁡(7+u) = -1 Round your answer to 1 decimal place
u = -7.0
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