Logarithmic Functions and Their Properties

Professor Dave explains logarithms, their role as inverse operations to exponents, and how to solve logarithmic equations. He also covers graphing logarithmic functions and their transformations, emphasizing the importance of understanding the relationship between exponential and logarithmic forms.

What is the inverse operation of exponentiation?

• Logarithm

• Division

• Subtraction

• Root extraction

If log base B of X equals Y, what does this imply?

• Y to the power of B equals X

• X to the power of B equals Y

• B to the power of X equals Y

• B to the power of Y equals X

What is the value of X in the equation log base 2 of 16 equals X?

• 2

• 3

• 4

• 5

How can you express B squared equals 9 in logarithmic form?

• log base 9 of B equals 2

• log base B of 9 equals 2

• log base 2 of B equals 9

• log base 2 of 9 equals B

What is the result of log base 7 of 1/49?

• 2

• -2

• 1/2

• -1/2

What is the domain of a logarithmic function?

• All real numbers

• Positive real numbers

• Negative real numbers

• Non-negative real numbers

What transformation occurs when a number is added outside the log function?

• Vertical shift

• Reflection across the X-axis

• Horizontal shift

• Reflection across the Y-axis

What happens to the graph of a logarithmic function when a negative sign is applied to the entire log term?

• It shifts vertically

• It shifts horizontally

• It reflects across the X-axis

• It reflects across the Y-axis

Which point does the graph of log base 2 of X pass through?

• (1, 1)

• (0, 0)

• (1, 0)

• (0, 1)

What is the range of a logarithmic function?

• All real numbers

• Non-negative real numbers

• Negative real numbers

• Positive real numbers