Introduction to Evaluating Logarithms Using Exponentials

This video tutorial teaches how to evaluate logarithms using exponentials. It covers inverse functions, explaining how x and y values switch, and reviews squares and square roots as inverses. The video also discusses logarithmic functions as inverses of exponentials, emphasizing the importance of keeping bases the same. Graphing of exponential and logarithmic functions is demonstrated, highlighting their asymptotes. Finally, the tutorial provides examples of solving logarithmic equations.

What happens to the x and y values in an inverse function?

• They are multiplied by 2.

• They remain the same.

• They are divided by each other.

• They are switched.

Which of the following is true about the notation f^(-1)(x)?

• It is the integral of f.

• It is the same as 1/x.

• It is the derivative of f.

• It represents the inverse of function f.

What is the inverse operation of squaring a number?

• Multiplying by 2

• Adding 2

• Taking the square root

• Dividing by 2

If 2^3 = 8, what is log base 2 of 8?

• 2

• 3

• 4

• 1

What is the inverse of an exponential function?

• A logarithmic function

• A cubic function

• A quadratic function

• A linear function

What type of asymptote does a logarithmic function have?

• No asymptote

• Horizontal on the x-axis

• Vertical on the y-axis

• Diagonal on the line y = x

How do you solve the equation 10^(x-1)/3 = 7?

• Multiply by 3, take the log, add 1

• Multiply by 7, take the log, add 1

• Divide by 7, take the log, subtract 1

• Divide by 3, take the log, subtract 1