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Logs!
Exponentials!
Applications!
Exponential EQ's!
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

Population Growth of Ghana. In 2014, the population of Ghana, located on the west coast of Africa, was about 25.8 million, and the exponential growth rate was 2.19% per year. Find the exponential growth function.

What is P(t)=25.8e^0.0219t?

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

Suppose that a stock’s price is rising at the rate of 7% per year, and that it continues to increase at this rate. If the value of one share of this stock is $43 now, find the value of one share of this stock three years from now.

What is $52.68?

𝑦=43(1.07)^3=$52.68

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

Suppose $2000 is invested in an account which offers 7.125% compounded monthly. Using compound interest formula, how much is in the account after 55 years?

What is $2852.92?

𝐴(𝑑)=2000(1+0.07125/12)^12𝑑=2000(1.0059375)^12𝑑

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

Rewrite: log(x^2y)




What is 2log(x)+log(y)?

400
Is the graph y= .7^x increasing or decreasing, and is it a function?
What is decreasing and yes, a function?
400

A video posted on YouTube initially had 80 views as soon as it was posted. The total number of views to date has been increasing exponentially according to the exponential growth function 𝑦=80𝑒^0.2𝑑, where t represents time measured in days since the video was posted. How many days does it take until 2500 people have viewed this video?

What is about 28.7 days ?

400

Solve: 2^(3x-7)=2^5

What is x= 4 ?

400
Solve: 3 ln x - 7 = 4 Round your answer to two decimal places.
What is x= 39.12 ?
500

Simplify: 3log_2(x) – 4log_2(x + 3) + log_2(y)

What is log_2((x^3y)/(x+3)^4) ?

500
Simplify ln e ^(3x)
What is 3x?
500

Consider the population of bacteria growing by the function f(t)=200e^0.02t, where t is measured in minutes. How many bacteria are present in the population after 55 hours? When does the population reach 100,000 bacteria?

What is 80,868 bacteria and 310.73 minutes?

500
Solve: 10^(2x+1) + 2 = 4 Round your answer to two decimal places.
What is x = -0.35 ?
500

Solve: log(⁑x)+log⁑(x+3)=1

What is x=2 ?