Exponential/Logarithm Test Review Game

Logs!

100

Simplify the expression: log₂8

What is 3?

200

Write the equation log₃729 = 6 in exponential form.

What is 3⁶=729 ?

300

Write the equation log 1000 = 3 in exponential form.

What is 10³=1000 ?

400

What is the asymptote of the graph of f(x) = log(x - 1) ?

What is x=1 ?

500

What is the asymptote of the graph of f(x)= log(x + 2) -1 ?

What is x= -2 ?

Exponential EQ's

100

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

What is log₄1,024 = 5 ?

200

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

What is log₂₇3 = 1/3 ?

300

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

What is log_1/28 = -3

400

Is the graph y= .7^x increasing or decreasing, and is it a function?

What is decreasing and yes, a function?

500

Simplify lne^3x

What is 3x?

Word Problems

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?

200

If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, after how many whole hours will you reach approximately 5,850 bacteria?

What is 3 hours?

300

A $50 investment is placed into a college savings fund for a child earning 8% interest compounded quarterly. If the child was born the day the money was invested and won't have access to the account until they turn 18, how much money will they have available for college tuition?

What is $208.06?

400

A $240,000 loan is taken out in the year 2020 at a 2.5% interest rate compounded continuously. How much interest will the borrower have to pay back in 2035?

What is $109,197.94 ?

500

The value of a certain car in 2015 was $45,000. If the car depreciates at a rate of 3.5% annually, approximately how long, to the nearest whole year, will it take for the car to reach half of its original value?

Hint: What would half the original value be? Set the equation equal to that number and solve for t.

What is 19 years?

Solving Exponential EQ's

100

Solve: 8^2x=8^x+7

What is x=7?

200

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

What is x=-9 ?

300

Solve: e^2x=e^x+4

What is x=4?

400

Solve: 3e^3-x= 15 Round your answer to two decimal places.

What is x= 1.39 ?

500

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

What is x = -0.35 ?

Solving Log EQ's

100

Solve: log x = 3

What is 1000?

200

log₃x = 5

What is x = 243 ?

300

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

What is x= 54.60 ?

400

Solve: 3 ln x - 7 = 4 Round your answer to two decimal places.

What is x= 39.12 ?

500

Solve: ln60 - ln4 = ln(x²+2x)

Hint: two answers

What is x=-5 and x = 3 ?