Solving Exponential Equations with Common Bases

The video tutorial covers solving exponential equations using common bases. It begins with an introduction to the topic and outlines the learning objectives. The instructor presents guiding questions and simple examples, gradually moving to more complex problems. Emphasis is placed on understanding exponent rules and applying them to solve equations. The video concludes with advanced examples, a summary, and prompts for student reflection.

What is the essential question for solving exponential equations using common bases?

• How can I check my answer?

• How can I rewrite each equation?

• What do both sides need to be equal?

• What is the value of x?

If the bases are the same, what equation can you write and solve for 2^(x+1) = 2^9?

• x = 8

• x = 9

• x + 1 = 9

• x + 1 = 8

What is the value of n in the equation 5^(4n + 5) = 5^(n - 7)?

• n = 4

• n = -5

• n = 5

• n = -4

How can you rewrite 36 to have a base of 6?

• 6^3

• 6^1

• 6^4

• 6^2

What is the value of P in the equation 2^(P-7) = 2^3?

• P = 4

• P = 3

• P = 10

• P = 7

How can you rewrite 1/7 to have a base of 7?

• 7^2

• 7^0

• 7^1

• 7^-1

What is the value of x in the equation 27^(2x + 6) = 3^(2x)?

• x = 4.5

• x = -4.5

• x = -9

• x = 9

What is the common base for the equation 25^(3y) = 125^(2)?

• 5

• 25

• 125

• 10

What is the value of x in the equation 4^(6x + 18) = 1/16?

• x = -5

• x = 5

• x = -2

• x = 2

What is a common mistake students make when solving exponential equations?

• Using the wrong exponent rules

• All of the above

• Forgetting to check their answer

• Not rewriting the bases