What is one to one property and how to use it to solve exponential and logarithmic eqn

The video tutorial explains the one-to-one property for both exponents and logarithms. It begins with an introduction to the concept, followed by detailed examples of how the property applies to exponential equations. The tutorial also covers more complex cases where the bases are not initially the same and demonstrates how to manipulate equations to apply the one-to-one property. Finally, the video explains the one-to-one property for logarithms, providing examples to illustrate the concept.

What does the one-to-one property state for exponential equations?

• If B^X = B^Y, then X = Y

• If B^X = B^Y, then X > Y

• If B^X = B^Y, then X < Y

• If B^X = B^Y, then X ≠ Y

How can you apply the one-to-one property when the bases are not the same?

• Change the base to a common number

• Add a constant to both sides

• Multiply both sides by a constant

• Subtract a constant from both sides

What must be done before using the one-to-one property if an exponent is multiplied by a number?

• Divide the exponent by the number

• Multiply the exponent by the number

• Add the number to both sides

• Isolate the exponent

Why can't the one-to-one property be used when the base cannot be rewritten as a power of another base?

• Because the property requires division

• Because the property requires subtraction

• Because the property requires addition

• Because the property only works with matching bases

What is the one-to-one property for logarithms?

• Log base B of X = Log base B of Y implies X ≠ Y

• Log base B of X = Log base B of Y implies X = Y

• Log base B of X = Log base B of Y implies X > Y

• Log base B of X = Log base B of Y implies X < Y

In a logarithmic equation, when can you set the arguments equal to each other?

• When the logs have the same base

• When the logs have different bases

• When the logs are multiplied by a constant

• When the logs are added together

What is a necessary condition for using the one-to-one property in logarithmic equations?

• The logs must be added together

• The logs must have the same base

• The logs must be multiplied by a constant

• The logs must have different bases