Solving Exponential Equations with Common Bases

The video tutorial covers solving exponential equations using common bases. It begins with an introduction to the lesson objectives and essential questions. The instructor provides examples of solving equations with the same base, emphasizing the importance of exponent rules. Advanced techniques are demonstrated for equations with different bases. The tutorial concludes with a summary and encourages students to reflect on common mistakes and their understanding of the topic.

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

• How to rewrite the equation?

• What do both sides need to be equal?

• What are the exponent rules?

• How to find the value of x?

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

• x + 1 = 8

• x = 9

• x + 1 = 9

• x = 8

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

• n = 4

• n = 11

• n = -4

• n = -11

When multiplying bases, what should you do with the exponents?

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

• Add the exponents

What is the value of k in the equation 3^(k+k+2) = 3^(5k-1)?

• k = 2

• k = 1

• k = -1

• k = 0

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

• 6^0

• 6^1

• 6^2

• 6^3

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

• p = 10

• p = -7

• p = 7

• p = 3

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

• 7^-1

• 7^0

• 7^1

• 7^2

What is the value of y in the equation 4^(y-3) = 16?

• y = 4

• y = 8

• y = 2

• y = 1

What should you do if you encounter a base in the denominator?

• Raise it to a positive power

• Raise it to a negative power

• Move it to the numerator

• Move it to the denominator