Solving Exponential and Quadratic Equations

This video tutorial focuses on solving exponential equations by expressing both sides with a common base, avoiding the use of logarithms. It covers several examples, demonstrating how to rewrite equations with common bases and solve for the variable. The video also introduces a quadratic equation example, showing how to factor and find solutions. The next video will cover solving these equations using logarithms.

What is the main focus of this video on exponential equations?

• Deriving exponential formulas

• Using logarithms to solve equations

• Solving equations with a common base

• Graphing exponential functions

In the first example, what is the value of x when 2^x equals 2^5?

• x = 3

• x = 4

• x = 2

• x = 5

Tags

CCSS.6.EE.A.1

How is the number 27 rewritten in the second example to find a common base?

• 5^3

• 2^3

• 3^3

• 4^3

What is the solution for x in the equation 3^(2x) = 3^(3x + 3)?

• x = -1

• x = -2

• x = -4

• x = -3

In the third example, what is the common base used to solve the equation involving 8 and 16?

• Base 5

• Base 2

• Base 3

• Base 4

What is the value of x when solving the equation 2^(6x) = 2^(16x + 20)?

• x = -4

• x = -3

• x = -2

• x = -1

Tags

CCSS.6.EE.A.1

In the final example, what is the rewritten form of 125?

• 5^3

• 5^2

• 5^4

• 5^5

Tags

CCSS.8.EE.A.2

What type of equation is solved in the final example?

• Linear equation

• Exponential equation

• Quadratic equation

• Cubic equation

Tags

CCSS.HSA-REI.B.4B

What are the solutions for x in the quadratic equation x^2 - 6x + 8 = 0?

• x = 4 and x = 2

• x = 3 and x = 4

• x = 2 and x = 3

• x = 1 and x = 2

What technique is highlighted in the video for solving exponential equations without logarithms?

• Finding a common base

• Applying the quadratic formula

• Using substitution

• Using a graphing calculator