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

A dangerous bacterial compound forms in a closed environment but is immediately detected. An initial detection reading suggests the concentration of bacteria in the closed environment is 1% of the fatal exposure level. 

This bacteria is known to double in concentration in a closed environment every hour and can be modeled by the function 

f(T) = 100 x 2T



What does the 100 mean and the 2 mean in the equation that represents this scenario?

The 100 is the number of bacteria detected at the 1% level 


The 2 represents the bacteria doubling every hour

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

A dangerous bacterial compound forms in a closed environment but is immediately detected. An initial detection reading suggests the concentration of bacteria in the closed environment is 1% of the fatal exposure level.

This bacteria is known to double in concentration in a closed environment every hour and can be modeled by the function

f(T) = 100 x 2T   


How much bacteria will be present when it is 100% fatal?


10,000 bacteria will be 100% fatal
200
Solve: 25^(x-4)=5^3x+1)
What is x=-9 ?
200
log (base 3) x = 5
What is x = 243 ?
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
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?
300
Solve: e^(2x)=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
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 ?
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
Simplify ln e ^(3x)
What is 3x?
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?
500
Solve: 10^(2x+1) + 2 = 4 Round your answer to two decimal places.
What is x = -0.35 ?
500

Automobile license plates typically have a combination of letters (26) and numbers (10).

In Oregon we assign a combination of 3 letters then 3 numbers for the standard license plate.  How many cars can the DMV assign a unique license plate to?

1,757,600 cars


log26(x) = 3   263 = x

log(x) = 3      103 = x


263 x 1000

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