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 45= 1,024 in logarithmic form.

What is log 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

Solve: 25^(x-4)=5^3x+1)

What is x=-9 ?

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 M = log (I/I0) , where M is the measurement of the Richter scale and I/I0 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: e2x=ex+4

What is x=4?

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

Use the formula M = log (I/I0) , where M is the measurement of the Richter scale and I/I0 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: 3e3-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
Simplify ln e ^(3x)
What is 3x?
500

Use the formula M = log (I/I0) , where M is the measurement of the Richter scale and I/I0 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: 102x+1+ 2 = 4 Round your answer to two decimal places.

What is x = -0.35 ?

500

Solve: log25(x2-4)=1/2 Hint: two answers

What is x=3 and x = -3 ?

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