Exponential/Logarithm Test Review Game

Logs!

100

Simplify the expression: log ₂ 8

What is 3?

200

Write the equation log ₃ 729 = 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 log (base 4) 1,024 = 5 ?

200

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

What is log ₂₇ 3 = 1/3 ?

300

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

What is log _1/2 8 = -3

400

Is the graph y= 0.7^x increasing or decreasing, and is it a function?

What is decreasing and yes, a function?

500

Simplify ln e^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.

Formula: f(t)=a(1+r)^t 

a- initial amount 

r - rate 

t- time 

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 hours will you reach approximately 5,850 bacteria?

Formula: f(t)=a(1+r)^t 

a- initial amount 

r - rate 

t- time 

What is 3 hours?

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?

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 ?

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?

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=-5 ?

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

Solve for x:  log₃ x = log₃ 2

What is x = 2 ?

300

Solve: ln x - ln 1 = ln (2x-3) 

What is x= 3 ?

400

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

What is x= 39.12 ?

500

Solve: log ₂ (x²) = 2  

x = -2,2