Logs!
Exponential EQ's
Word Problems
Solving Exponential EQ's
Solving Log EQ's
100
Simplify the expression: 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? Round to the nearest whole number.
What is 9,155 bacteria?
100
Solve: 8^(2x)=8^(x+7)
What is x=7?
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
If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, after how many hours will you reach approximately 5,850 bacteria?
What is 3 hours?
200

book 1 - 309 pages

book 2 - 352 pages

book 3 - 448 pages

book 4 - 734 pages

book 5 - 870 pages

Find an exponential model that fi ts this data, where y is the number of pages in book x.

y = 215.3(1.324)x

200

log 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

If h(x) = ln(x) then h-1(x) = ? .

ex

300
Solve: ln x = 4 Round your answer to two decimal places.
What is x= 54.60 ?
400

Write as a single log:

3log 2 + 5log x - 2log y

What is log (8x5/y2)?

400
Is the graph y= .7^x increasing or decreasing, and is it a function?
What is decreasing and yes, a function?
400

The amount of a particular drug in a person’s bloodstream decreases by 12% per hour after taking the drug. Suppose Alicia takes an initial dose of 400 mg.  Find the amount of drug in her bloodstream, to the nearest milligram, 4 hours after she took the initial dose.

What is 240 mg?

400
Solve: 3e^(3 - x)= 15 Round your answer to two decimal places.
What is x= 1.39 ?
400
Solve: 3 ln x - 7 = 4 Round your answer to two decimal places.
What is x= 39.12 ?
500

Solve: log 8 x = 1/3

What is x= 2?

500
Simplify ln e ^(3x)
What is 3x?
500

The pH scale measures the strength of acids and bases. Its formula is pH = –log(H +) where H + is the concentration of hydrogen ions. A substance with a lower pH is more acidic. The pH of normal rain water is somewhere between 5.0 and 5.6. The pH of acid rain falling in the Great Smoky Mountains National Park is 4.7. The rain in the park is how many times as acidic as normal rain water? Give a range for your answer:

“Between ? and ? times as acidic.”

What is between 2 and 8?

500
Solve: 10^(2x+1) + 2 = 4 Round your answer to two decimal places.
What is x = -0.35 ?
500

Give the exact answer using logs

1.5x = 12

log 12 / log 1.5

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