Exponential Equations and Exponents

This video is the first in a series exploring how to solve exponential and logarithmic equations. It focuses on solving exponential equations by changing the base to a common base. The video provides three examples: one with bases 3 and 27, another with bases 32 and 4, and a final example involving fractions and negative exponents. The technique involves rewriting numbers as powers of a common base, simplifying the equation, and solving for the variable.

What is the main focus of this video series?

• Solving trigonometric equations

• Solving linear equations

• Solving exponential and logarithmic equations

• Solving quadratic equations

How many videos are dedicated to solving exponential equations in this series?

• Four

• Three

• One

• Two

What is the main focus of the video series?

• Solving trigonometric equations

• Solving linear equations

• Solving exponential and logarithmic equations

• Solving quadratic equations

How many videos are dedicated to solving exponential equations in this series?

• Three

• Two

• Four

• One

What is the first step in solving exponential equations by changing the base?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Make the bases match

What is the first step in solving exponential equations by changing the base?

• Add the exponents

• Subtract the exponents

• Make the bases match

• Divide the exponents

In the first example, what is the common base used for the numbers 3 and 27?

• 2

• 3

• 4

• 5

What is the exponent of 3 when 27 is rewritten as a power of 3?

• 2

• 3

• 4

• 5

After matching the bases in the first example, what equation do we solve?

• 4x + 5 = 2x

• 4x - 5 = 2x

• 4x + 5 = 3x

• 4x - 5 = 3x

What is the solution for x in the first example problem?

• x = 3

• x = 4

• x = 5

• x = 6