Use the change of base formula to evaluate the logarithmic function. Round to two decimal places.
log(base 6)13
What is 1.43?
100
Mrs. Meredith deposits $2,000 in a bank account. How much money will she have if she has an interest rate of 6.5%, and it is calculated continuously for three years? Round your answer to 3 decimal places if necessary.
What is $2,430.622?
100
ln (x) = 4
What is x = 54.598?
100
Where was the mathematician Euler from?
What is Switzerland?
200
Evaluate the function f(x) = 6.1^(x) if x = 2.4
What is 76.699?
200
Write the logarithmic function as an exponential function.
log 1000 = 3
What is 10^(3) = 1000?
200
Mrs. Ralph deposits $2,000 in a bank account. How much money will she have if it has an interest rate of 6.5%, and is calculated annually for 3 years? Round your answer to 3 decimal places if necessary.
What is $2,415.899?
200
e^(3x) = 25
What is x=1.073?
200
Pi is the ratio of a circle's circumference to its
What is diameter?
300
Describe the shifts to get from f(x) to g(x) if f(x) = 4^(x) and g(x) = 4^(x-1) - 3.
What is the graph is shifted 3 units down and 1 unit right?
300
Use properties of logarithms to expand the expression.
ln(5x^3)
What is ln5 + 3lnx?
300
Mrs. Meredith buys a car for $25,000. The car depreciates at a rate of 6.75%. How much is the car worth after two years?
What is $21,738.91?
300
e^(4x) = e^(x^2 +3)
What is x=1,3?
300
List 3 notations/ideas credited to Euler:
What is f(x), sigma, function, e, i
400
Write the exponential function as a logarithmic function. 2^(4) = 16
What is log(base 2)16 = 4?
400
What is the domain of y = log (base 3) x?
What is all positive numbers?
400
Phosphorus-32 has a half-life of 27 days. You have a 50 mg sample. How much Phosphorus-32 remains after 100 days?
What is 3.85 mg?
400
6^(x) - 28 = -8
What is x=1.672?
400
List three real-world applications of logs:
What is measuring earthquakes, measuring sound, measuring pH
500
Write the exponential function as a logarithmic function. 5^(0) = 1
What is log base 5 of 1 = 0?
500
Find the domain, x-intercept, and range of the logarithmic function. f(x) = log (base 2) (x + 3)
What is domain (-3, infinity), x-intercept (-2, 0), and range (-infinity, infinity)?
500
Mrs. Ralph deposits $2,000 in a bank account. She earns 3.25% compounded continuously. How much money does she have after 7 years ?