Solving Exponential Equations and Properties

The video tutorial covers solving exponential equations using the properties of equality. It begins by explaining the concept of like bases and how to set exponents equal when bases are the same. The tutorial then demonstrates solving equations with base 3 and rewriting bases to solve equations with different bases, such as base 5 and base 125. Finally, it explores creative solutions involving fractions and like bases, providing step-by-step examples to illustrate the process.

What is the key property used to solve exponential equations when the bases are the same?

• Set the coefficients equal

• Set the exponents equal

• Divide the exponents

• Multiply the bases

In the equation 3^(5x) = 3^(2x + 2), what is the value of x?

• 1

• 1/2

• 2

• 3

In the context of exponential equations, what does 'plug and chug' refer to?

• Dividing the exponents

• Multiplying the bases

• Substituting values to verify the solution

• Adding the coefficients

When rewriting 125 as a power of 5, what exponent should be used?

• 5

• 2

• 3

• 4

In the equation 5^(6x + 1) = 5^(3x + 3), what is the value of x?

• 1/3

• 2/3

• 3/2

• 1/2

What is the common base used to solve the equation involving 8 and 2?

• 4

• 16

• 2

• 8

In the equation 2^(3x - 12) = 2^(-x - 3), what is the value of x?

• 9/4

• 4/9

• 3/4

• 1/4

What is the exponent of 2 when rewriting 1/2 as a power of 2?

• -1

• 2

• 0

• 1

Which property allows us to cancel out the bases when they are the same on both sides of an equation?

• Commutative Property

• Distributive Property

• Property of Equality

• Associative Property

What is the result of distributing 3 in the expression 3(x - 4)?

• 3x - 12

• 3x + 12

• 3x - 4

• 3x + 4