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Logs!
Exponential EQ's
Word Problems
Solving Exponential EQ's
Solving Log EQ's
100

Simplify the expression: log28

What is 3?

100

Write the exponential equation 45= 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: 2(2)x-3 + 1 =69

What is x=8.09

100

Solve: log x = 3

What is 1000?

200

Write the equation log3 729 = 6 in exponential form.

What is 3^6=729 ?

200

Write the exponential equation 271/3= 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

Solve: 0.05(1.18)x = 5

What is x=27.82 ?

200

log3x = 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

Solve: 6(x + 4) = 27

What is -2.5

300

Solve: ln x = 4 Round your answer to two decimal places.

What is x= 54.60 ?

400

What is the asymptote of the graph of f(x) = log(x - 1) ?

What is x=1 ?

400

Is the graph y= .7x increasing or decreasing, and what is the asymptote?

What is decreasing and yes, a function?

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

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

What is the asymptote of the graph of f(x)= log(x + 2) -1 ?

What is x= -2 ?

500

Solve, write the exact answer  e3x = 10

What is 3x?

500

Suppose that a new employee starts working at $7.89 per hour and receives a 3% raise each year. After time t, in years, his hourly wage is given by the equation    y =$7.89 left(1.03)t . Find the amount of time after which he will be earning $10.00 per hour. 

What is 8 years

500

Solve: x2x = 14

What is x = 1.32 ?

500

In 2007, a country had a population of 82,700 thousand. At that time, the country's population was declining at a rate of 0.036% per year. If this continues, how long will it take the country's population to reach 82,000 thousand? Use y = y0e-0.00036t. 

What is 23.6 years