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Logs!
Exponential EQ's
Word Problems
Solving Exponential EQ's
Find the Inverse
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: 2^x = 0.125

What is x=-3?

100

Find the Inverse of: f(x)=3(x-1)+2

What is y=(x-2)/3 - 1?

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: 4^(n-2) +5 = 13

What is n=3.5 ?

200

Find the Inverse of: f(x)=-(x-9)^2 +3 on the interval x>9

What is y= sqrt(-x+3) +9

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

You currently have a total of 54 peppers growing on your pepper plants. If you plan to harvest 16% of the peppers every day, how many days will it take before there are only 20 peppers left?

What is 5.69 days?

300

Solve: 5^(2x)=5^(x+4)

What is x=4?

300

Find the Inverse of: y=10(2)^x

What is y=log(base 2) (x/10) ?

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

Suppose the population of a country is currently 8,100,000. The population is increasing by 2% each year. How long would it take for this country's population to reach 9 million?

What is 5.32 yrs ?

400

Solve: 3(2)^(3 - x)= 15 Round your answer to two decimal places.

What is x= 0.68 ?

400

Find the Inverse of: y= 3(4)^(x-6)

What is y=log(base 4)(x/3)+6 ?

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

Simplify log (10 ^(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

Find the Inverse of: g(x)=log(base 2)(x)+2

What is y=(2)^(x-2) ?