Solving Exponential equations

The video tutorial explains the one-to-one properties of exponents, which state that if two expressions with the same base are equal, their exponents must also be equal. The instructor provides examples using different bases to illustrate this concept. Finally, the video demonstrates how to apply these properties to solve equations by equating the exponents and isolating variables.

What is the main idea behind one-to-one properties?

• If two expressions have the same base, their exponents must be different.

• If two expressions have the same base, their exponents must be equal.

• If two expressions have different bases, their exponents must be equal.

• If two expressions have different bases, their exponents must be different.

In the example 2^2 = 2^x, what is the value of x?

• 3

• 4

• 1

• 2

What does the example 10^2 = 10^x demonstrate?

• The bases must be equal if the exponents are different.

• The exponents must be equal if the bases are the same.

• The exponents must be different for the bases to be equal.

• The bases must be different for the exponents to be equal.

How do you solve an equation using one-to-one properties?

• By making the bases different.

• By setting the bases equal when the exponents are different.

• By making the exponents different.

• By setting the exponents equal when the bases are the same.

What is the final step in applying one-to-one properties to solve an equation?

• Add a constant to both sides.

• Multiply both sides by the base.

• Change the base of the equation.

• Set the exponents equal to each other.