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

Simplify the expression: log2 8

What is 3?

100

Write the exponential equation 45= 1,024 in logarithmic form.

What is log4 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: 82x=8(x+7)

What is x=7?

100

Solve: log x = 3

What is 1000?

200

Write the equation log3 729 = 6 in exponential form.

What is 36 = 729 ?

200

Write the exponential equation 27(1/3) = 3 in logarithmic form.

What is log27 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: 25(x-4)=5(3x+1)

What is x=-9 ?

200

log3 x = 5

What is x = 243 ?

300

Write the equation log 1000 = 3 in exponential form.

What is 103 = 1000 ?

300

Write the exponential equation (1/2)-3=8 in logarithmic form.

What is log1/2 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: e(2x)=e(x+4)

What is x=4?

300

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

What is x= 54.60 ?

400

Simplify the log expression: log4 (1/64)

What is x = -3 ?

400

Simplify log 102

What is x = 2?

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

Simplify the expression: log 10,000

What is x= 4 ?

500

Simplify ln e3x

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 your answer to four decimal places.
What is 36,897,759.8570?
500

Solve: 10(2x+1) + 2 = 4 Round your answer to two decimal places.

What is x = -0.35 ?

500

Solve: log(5x) + log(x-10) = 3

What is x=20 ?

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