Exponential/Logarithm Summer 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 10^3=1000 ?

400

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

What is x=1 ?

500

If log₂ b = c, then find log₄b in terms of c

What is c/2 ?

Log Rules

100

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

What is log₄1,024 = 5 ?

200

Simplify ln e^3x

What is 3x?

300

If log_ba=0.82, then the value of log_b(b/a) is what?

What is 0.18?

400

Simplify into one log:  2log_a5+log_a6- 1/3 log_a8.

What is log_a75?

500

The value of the summation of n = 1 to 9 of the expression log (n/(n+1)).

What is -1?

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

A city population of 15000 decreases by 8% each year.  How many years will it take for the population to become 5000? (round to 1 decimal place)

What is 13.2 years?

300

An earthquake in Turkey measured 5.2 on the Richter Scale. It is 2500 times strong than an earthquake in Burnaby.  What was the Richter Scale measure of the Burnaby earthquake?

What is 1.8?

400

The price of a particular product doubles every 35 years.  If the price of the product was $16.40 on January 1996, then the price of the product will be $336.50 in which year?

What is 2036 ?

500

A ball is dropped from a height of 5 metres.  After each bounce, it rises to 60% of its previous height.  What is the total vertical distance the ball travels before it comes to rest?

What is 20 metres?

Exponentials

100

Is the graph y= (0.7)^x increasing or decreasing?

What is DECREASING?

200

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

What is x=-9 ?

300

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

What is x=1.39?

400

How many terms are in the geometric series with a sum of 32752, where the first term is 16 and common ratio of 2?

What is 11 terms ?

500

Solve (1/2)^x-1 = 3^x to three decimal places.

What is x = 0.387?

Solving Log EQ's

100

Solve: log x = 3

What is 1000?

200

log₃x = 5

What is x = 243 ?

300

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

What is x= 39.12 ?

400

Solve: log₅(2x+1)+log₅(x+2)=1

What is x= 1/2 ?

500

If log₃(2x-y)=2 and log₂(x+2y)=5, find y.

What is y=11 ?