Logarithms and Exponential Functions

The video tutorial explains how to find the inverse of a function, specifically f(x) = log base 2 of x. The process involves swapping the variables x and y, and then solving for y. The tutorial demonstrates converting the logarithmic form to exponential form, resulting in the inverse function f inverse of x = 2 raised to the x. The key takeaway is understanding that logarithms and exponentials are inverses of each other.

What is the initial function given in the tutorial?

• f(x) = log base 10 of x

• f(x) = log base 2 of x

• f(x) = x^2

• f(x) = 2^x

What is the base of the logarithm in the function f(x) = log base 2 of x?

• e

• 10

• x

• 2

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

• Integrate the function

• Differentiate the function

• Swap the x and y variables

• Convert to exponential form

What does swapping the x and y variables help achieve?

• It helps find the derivative

• It helps find the inverse function

• It helps integrate the function

• It helps solve for x

How do you solve an equation with a logarithm for y?

• By adding a constant

• By differentiating both sides

• By converting it to exponential form

• By integrating both sides

What is the exponential form of the equation y = log base 2 of x?

• y^2 = x

• 2^x = y

• x^2 = y

• 2^y = x

What is the result of converting the logarithmic equation to exponential form?

• A trigonometric equation

• A linear equation

• A polynomial equation

• An exponential equation

What is the purpose of converting a logarithmic equation to exponential form?

• To simplify the equation

• To integrate the equation

• To solve for y

• To find the derivative

What is the inverse function of f(x) = log base 2 of x?

• f^(-1)(x) = 2^x

• f^(-1)(x) = x^2

• f^(-1)(x) = x/2

• f^(-1)(x) = log base 2 of x

What is the relationship between logarithms and exponentials?

• They are unrelated

• They are inverses of each other

• They are the same

• One is the derivative of the other