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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

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

What is x=-9 ?

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

If you invest $3,000 in a savings account with a 0.5% interest rate compounding continuously, how much money will be in your account after 2 years? Round to the nearest penny.

What is $3030.15.

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

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 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

The transformation of 

log (base 7) x 

compared to ln(x). 

Round to nearest thousandth if needed.

What is vertical compression by 0.514?

500

Simplify:

 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 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

The HAs for the logistic equation with an initial value of 30 and a ceiling of 150.

Hint: use the proper format

What is y=0 and y=150 ?