Logarithms and Their Properties

This video tutorial covers logarithms, including how to evaluate them, their properties, and the change of base formula. It also explains how to solve logarithmic equations and graph logarithmic and exponential functions. The tutorial concludes with solving word problems related to compounded interest and population growth using logarithms and exponential functions.

What is the value of log base 2 of 32?

• 6

• 5

• 3

• 4

Which of the following is the correct change of base formula for log base a of b?

• log b / log a

• log a / log b

• ln a / ln b

• ln b / ln a

How can you express log base a of b + log base a of c as a single logarithm?

• log base a of (c / b)

• log base a of (b / c)

• log base a of (b * c)

• log base a of (b + c)

If log base 5 of (10x - 5) equals 2, what is the value of x?

• 3

• 6

• 5

• 4

What is the solution to the equation 4^(2x - 1) = 8^(3x + 2)?

• x = -1

• x = 1

• x = 8/5

• x = -8/5

What is the solution for x in the equation e^x = 5?

• x = ln(5)

• x = 1/5

• x = e^5

• x = 5

When graphing the exponential function y = 2^x - 3, what is the horizontal asymptote?

• x = -3

• y = 0

• y = -3

• x = 0

For the logarithmic function log base 2 (x - 1) + 3, what is the vertical asymptote?

• x = 0

• x = 1

• y = 0

• y = 1

If an investment is compounded monthly at an 8% annual interest rate, how many times is interest applied in a year?

• 52 times

• 8 times

• 12 times

• 24 times

Using the rule of 72, how long will it take for an investment to double at a 9% interest rate?

• 10 years

• 7 years

• 9 years

• 8 years