Understanding Domains of Logarithmic Functions

This video tutorial explains how to find the domain of various logarithmic functions. It covers multiple examples, including functions with different bases and expressions inside the logarithm. The video demonstrates how to set the expression inside the logarithm greater than zero and solve for the domain using number lines and factorization techniques.

What must be true about the argument of a logarithmic function for it to be defined?

• It can be any real number.

• It must be less than zero.

• It must be equal to zero.

• It must be greater than zero.

For the function log base 3 of (x + 5), what is the domain?

• x < -5

• x = -5

• x > -5

• x ≥ -5

How do you determine the domain of a function like log base 3 of (3x - 5)?

• Set 3x - 5 equal to zero.

• Set 3x - 5 greater than zero.

• Set 3x - 5 less than zero.

• Set 3x - 5 not equal to zero.

What is the domain of the function log base 3 of (4 - 2/3x)?

• x = 6

• x > 6

• x < 6

• x ≤ 6

When factoring x^2 - 9 in a logarithmic function, what values must be excluded from the domain?

• x = 9 and x = -9

• x = 3 and x = -3

• x = 0 and x = 9

• x = 0 and x = -9

For the function log base 2 of (x - 1)^2, what is the domain?

• x < 1

• x > 1

• x ≠ 1

• x = 1

In the function log base 7 of (x^2 - 4x), which values of x are not allowed?

• x = 0 and x = 4

• x = 2 and x = -2

• x = 4 and x = -4

• x = 0 and x = -4

For the function log base 2 of (x + 4)/(x - 4), what is the domain?

• x = 4

• x < 4

• x > 4

• x ≠ 4 and x ≠ -4

What is the domain of the function log base 9 of (2 - x)/(x + 3)?

• -3 < x < 2

• x < -3

• x > 2

• x = 2

For the function log base 4 of (x^2 - 3x - 10), what is the domain?

• x = -2 or x = 5

• x ≠ -2 and x ≠ 5

• x < -2 or x > 5

• x > -2 and x < 5