Exponential Equations and Their Solutions

Mrs. Yaod introduces solving exponential equations, focusing on equations where the variable is in the exponent. She explains the rule that if the bases are the same, the exponents must be equal. The lesson includes examples and practice problems, demonstrating how to solve equations with both same and different bases. Students are encouraged to solve problems independently and verify their solutions. The video concludes with advanced problems, emphasizing the importance of understanding the underlying concepts.

What is an exponential equation?

• An equation with only constants

• An equation with no variables

• An equation where the variable is in the exponent

• An equation where the variable is in the base

If 2^x = 2^5, what is the value of x?

• x = 0

• x = 5

• x = 2

• x = 10

Why can't the base b be equal to 1 in an exponential equation?

• Because it makes the equation unsolvable

• Because it results in multiple solutions for x

• Because it makes the equation linear

• Because it results in no solution

In the equation 6^(4x-5) = 6^(2x), what is the value of x?

• x = 1.5

• x = 0

• x = 5

• x = 2.5

How can you verify your solution to an exponential equation?

• By checking if the bases are different

• By multiplying both sides by zero

• By substituting the solution back into the original equation

• By changing the base to 1

What is the first step when solving exponential equations with different bases?

• Subtract the exponents

• Find a common base

• Multiply the bases

• Add the exponents

If 4^(2x+11) = 1024, what is the value of x?

• x = 0

• x = 3

• x = -3

• x = 5

What is the exponent of 8 that results in 512?

• 3

• 5

• 4

• 2

In the equation 7^(2(x-2)) = 7^3, what is the value of x?

• x = 2

• x = 5

• x = 7/2

• x = 3.5

What happens when the variables disappear in an exponential equation?

• The equation is incorrect

• The equation has infinite solutions

• The equation has no solution

• The equation is linear