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

What is x=-5/2 ?

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

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

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

You put $2,000 into a bank account with a 4% nominal interest rate, compounded monthly. What will be the account balance after 3 years?

What is $2254.54 ?

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
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

Solve: 32 ln(15x) + 5 = 0

What is x = e^(-5/32) / 15 ?