Common Core Algebra 2: Method of Common Bases

The video tutorial by Kirk Wier covers the method of common bases in Algebra 2. It begins with an introduction to the concept, followed by exercises on solving exponential equations and simplifying expressions using common bases. The tutorial progresses to more challenging problems and includes a multiple choice question. An application problem involving the area of a rectangle is also discussed. The video concludes with a final problem and a summary of the method's utility in solving exponential equations.

What is the first step in solving the equation 2^x = 16 using the method of common bases?

• Subtract 2 from both sides

• Add 4 to both sides

• Divide both sides by 2

• Rewrite 16 as 2^4

If 3^x = 27, what is the value of x?

• 3

• 2

• 4

• 5

How can you simplify the expression (2^3)^x?

• 2^(3x)

• 2^(x+3)

• 2^(3/x)

• 2^(x-3)

What is the simplified form of (3^2)^(2x+1)?

• 3^(2x+1)

• 3^(4x+2)

• 3^(4x+1)

• 3^(2x+2)

In the equation 8^x = 32, what common base can be used to solve it?

• Base 3

• Base 2

• Base 4

• Base 5

What is the value of x in the equation 5^(3x) = 125?

• 1

• 2

• 4

• 3

Which of the following represents the solution set to 2^(x^2 - 3) = 64?

• x = ±4

• x = ±3

• x = ±5

• x = ±2

Why is the method of common bases not useful for solving 5^x = 8?

• Because 5 and 8 do not have a common base

• Because 5 is not a prime number

• Because 8 is not a prime number

• Because the equation is already simplified

What are the coordinates of the intersection point of the curves y = 4^(x+5) and y = 12^(2x+1)?

• (-3/2, -4)

• (3/2, 4)

• (-3/2, 4)

• (3/2, -4)

What is the area of the rectangle formed by the intersection point of the curves y = 4^(x+5) and y = 12^(2x+1)?

• 4

• 6

• 8

• 10