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

What is x=-9 ?

200

log (base 3) (9x-4) = log (base 3) (x+20)

What is x = 3 ?

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

  1. An adult takes 400 mg of Advil. Each hour, the amount of Advil in the adult's system decreases by about 29%. How much Advil will be left after 4 hours, to the nearest hundredth?

What is 101.65 mg?

300

Solve: 9^(a+2)=27^(4a-2)

What is a=1?

300

Solve: log (2y-10) = 7log 2 - log 8 .

What is y= 13 ?

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

In 2005, there were only 285 Pittsburgh Penguins fans in Oakville. The number of Penguins fans increased by 75% per year after 2005 (this is when Crosby was drafted). How many Crosby fans are now in Oakville in 2014?

What is 43,871 fans ?

400

Solve: 7-4^(x+1)= 18 Round your answer to two decimal places.

What is No Solution ?

400

Solve: log (base 36) (20-4p) = 1/2 Round your answer to two decimal places.

What is p= 3.5 ?

500
What is the asymptote of the graph of f(x)= log(x + 2) -1 ?
What is x= -2 ?
500

Simplify log (base 4) 4 ^(3x)

What is 3x?

500

The population of germs in a dirty bathtub doubles every 20 minutes. How long will it take for the population to triple? Write your answer to the nearest tenth.

What is 31.7 minutes?

500

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

What is x = -0.35 ?

500

Solve: log (2x) + log (x-5) = 2

What is x=10  ?

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