Logarithmic Functions

This video tutorial explains logarithmic functions, their relationship with exponentials, and their practical applications. It covers graphing exponentials and their inverses, converting between exponential and logarithmic forms, and understanding common and natural logarithms. The tutorial emphasizes the importance of practicing these conversions to solve logarithmic equations effectively.

What is the primary reason logarithms are still relevant today despite the availability of calculators?

• They are easier to use than calculators.

• They have a unique property called the power property.

• They are more accurate than calculators.

• They are faster than calculators.

What is the inverse of the function y = 2^x?

• y = log base 2 of x

• x = 2^y

• y = 2^y

• x = log base 2 of y

How would you express 2^3 = 8 in logarithmic form?

• log base 2 of 8 = 3

• log base 3 of 8 = 2

• log base 2 of 3 = 8

• log base 8 of 2 = 3

What is implied if a logarithm is written without a base?

• The base is 1

• The base is e

• The base is 10

• The base is 2

What is the natural logarithmic function's base?

• 10

• 1

• 2

• e