Finding Inverses of Logarithmic Functions

The video tutorial explains how to find the inverse of logarithmic functions. It begins with an introduction to inverse functions and the process of switching x and y. The tutorial then provides step-by-step examples, demonstrating how to isolate the log function, convert it to index form, and solve for y. Each example builds on the previous one, reinforcing the method and ensuring understanding.

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

• Change the base of the logarithm

• Switch x and y

• Multiply by the base

• Add a constant

What is the inverse of the function y = log_e(x)?

• y = x^e

• y = e^(-x)

• y = e^x

• y = log_x(e)

What is the inverse of y = log_e(x/2)?

• y = log_e(2x)

• y = e^x/2

• y = e^(x/2)

• y = 2e^x

What is the inverse of y = log_e(x/3)?

• y = log_e(3x)

• y = 3e^x

• y = e^(x/3)

• y = e^x/3

What is the inverse of y = log_e(x/4)?

• y = e^x/4

• y = e^(x/4)

• y = log_e(4x)

• y = 4e^x

What is the inverse of y = log_e(x/5)?

• y = log_e(5x)

• y = e^x/5

• y = e^(x/5)

• y = 5e^x

When converting from log form to index form, what becomes the base of the power?

• The power

• The coefficient

• The base of the log

• The subject

In the process of finding an inverse, what should you do after switching x and y?

• Add a constant to both sides

• Divide by the coefficient

• Change the equation to index form

• Multiply by the base

What is the inverse of y = log_e(x + 1)?

• y = e^x - 1

• y = log_e(x - 1)

• y = e^(x + 1)

• y = e^(x - 1)

What is the inverse of y = log_e(x + 4)?

• y = e^(x + 4)

• y = e^(x - 4)

• y = log_e(x - 4)

• y = e^x - 4