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

Evaluate the expression: log28

What is 3?

100

Write the exponential equation 45= 1024 in logarithmic form.

What is log41024 = 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 log3729 = 6 in exponential form.

What is 36=729 ?

200

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

What is log273 = 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

log3x = 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 log(1/2)8 = -3

300

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 9.3% per hour. How many hours does it take for the size of the sample to double? Note: This is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

What is 7.45?

300

Solve: e2x=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

Suppose that $3000 is placed in a savings account at an annual rate of 9.8%, compounded semiannually. Assuming that no withdrawals are made, how long will it take for the account to grow to $3462? Do not round any intermediate computations, and round your answer to the nearest hundredth.

What is 1.50 years?

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

Expand: log (x2yz)

What is 2logx+logy+logz

500

An initial amount of $2700 is invested in an account at an interest rate of 2.5% per year, compounded continuously. Assuming that no withdrawals are made, how many years will it take for the account to reach $2983.96? Do not round any intermediate computations, and round your answer to the nearest whole number.

What is 4 years?

500

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

What is x = -0.35 ?

500

Solve: 2log x = log (2x-4) + log 4

What is x=4?