Logarithmic Functions and Their Properties

This video tutorial provides a comprehensive review of logarithms, covering how to rewrite logs and exponentials, evaluate logs without a calculator, understand properties of logarithms, find inverses, and solve logarithmic equations. It serves as an overview for students at the end of a unit on logs, offering insights into key concepts and techniques.

What is the base of the logarithm in the expression log base B of C = D?

• B

• C

• D

• log

How can you rewrite the expression 4^3 = 64 in logarithmic form?

• log base 4 of 64 = 3

• log base 3 of 4 = 64

• log base 3 of 64 = 4

• log base 64 of 4 = 3

What is the result of log base 3 of 1/9?

• 3

• -2

• 2

• -3

When condensing logarithms, what does addition between logs become?

• Product

• Quotient

• Sum

• Difference

In expanding logarithms, what happens to a coefficient in front of a log?

• It is subtracted from the log

• It is added to the log

• It becomes a base

• It becomes an exponent

What is the first step in finding the inverse of a function?

• Rewrite in exponential form

• Replace f(x) with y

• Solve for y

• Switch x and y

What is the inverse of an exponential function?

• Trigonometric function

• Linear function

• Quadratic function

• Logarithmic function

How do you solve a logarithmic equation with the same base on both sides?

• Add the bases

• Set the arguments equal

• Subtract the arguments

• Multiply the exponents

What is the base of a natural logarithm?

• e

• 10

• π

• 2

In solving log base 3 of 4x + 1 = 4, what is the first step?

• Subtract 1 from both sides

• Rewrite as an exponential

• Add 1 to both sides

• Divide by 4