Solving Exponential Equations Techniques

This video tutorial focuses on solving exponential equations by expressing both sides with a common base, avoiding the use of logarithms. It provides multiple examples, demonstrating how to rewrite equations to have the same base and solve for the variable by equating exponents. The video covers equations with bases 2, 3, and 5, including a quadratic equation example. The next video will explore 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 by equating exponents with the same base

• Graphing exponential functions

In the first example, what is the value of x if 2^x = 2^5?

• x = 2

• x = 3

• x = 5

• x = 7

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

• 2^3

• 3^3

• 5^3

• 4^3

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

• x = -3

• x = -2

• x = -4

• x = -1

In the third example, what is the common base used to solve the equation?

• Base 2

• Base 5

• Base 3

• Base 4

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

• x = -3

• x = -2

• x = -4

• x = -1

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

• 5^5

• 5^2

• 5^3

• 5^4

What type of equation is solved in the final example?

• Cubic equation

• Quadratic equation

• Exponential equation

• Linear equation

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

• x = 3 and x = 4

• x = 2 and x = 3

• x = 1 and x = 2

• x = 4 and x = 2

What technique is highlighted in this video for solving exponential equations?

• Trial and error

• Common base technique

• Graphical method

• Using logarithms