Solving Exponential Equations in Algebra and Precalculus

The video tutorial explains how to solve an exponential equation involving powers of three. It begins by introducing the problem and then discusses the properties of exponents, such as multiplying with a common base and breaking down exponents. The tutorial demonstrates how to rewrite the equation using these properties and solve it step-by-step. The solution is verified by substituting the value back into the original equation, confirming the correctness of the answer.

What is the base in the equation discussed in the video?

• Base 5

• Base 3

• Base 10

• Base 2

What is the result of multiplying exponents with the same base?

• None of the above

• You divide the exponents

• You subtract the exponents

• You add the exponents

How can you express 3 raised to the power of (x+2)?

• 3^(x*2)

• 3^x + 3^2

• 3^x * 3^2

• 3^(x/2)

What is 81 expressed as a power of 3?

• 3^3

• 3^4

• 3^2

• 3^5

What does 3 squared equal?

• 9

• 12

• 6

• 15

What is the simplified form of 9 times 3^x + 3^x?

• 10 * 3^x

• 12 * 3^x

• 9 * 3^(x+1)

• 3^(x+2)

What happens to the exponent when you move a term from the denominator to the numerator?

• The exponent is halved

• The exponent doubles

• The exponent changes sign

• The exponent becomes zero

What is the value of x in the equation 3^x = 3^-4?

• x = 4

• x = -4

• x = 1

• x = 0

What property of exponents is used to solve the equation by equating the exponents?

• Product of powers property

• Power of a power property

• Power of a product property

• Quotient of powers property

How do you verify the solution of an exponential equation?

• Substitute the value of x back into the equation

• Multiply both sides by x

• Add the same number to both sides

• None of the above