Solving Logarithmic and Exponential Equations

The video tutorial explains how to solve equations involving logarithms by using inverse operations. It covers examples with different bases, including base 3, base 4, and natural logarithms (base e). The instructor demonstrates how to isolate variables by exponentiating both sides of the equation, emphasizing the inverse relationship between logarithms and exponentiation. The tutorial also provides step-by-step solutions to example problems, illustrating the process of solving for variables in logarithmic equations.

What is the main goal when solving a logarithmic equation?

• To isolate the variable

• To find the base of the logarithm

• To multiply both sides by the base

• To change the base of the logarithm

What is the inverse operation of taking a logarithm?

• Exponentiation

• Multiplication

• Subtraction

• Addition

In the equation log base 3 of 2x = 2, what is the result of exponentiating both sides with base 3?

• 2x = 6

• 2x = 12

• 2x = 3

• 2x = 9

After exponentiating both sides of the equation log base 3 of 2x = 2, what is the next step to solve for x?

• Multiply both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides

• Divide both sides by 2

In the equation -2 log base 4 of 3x = -2, what is the first step to isolate the logarithm?

• Divide both sides by -2

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply both sides by -2

What is the result of exponentiating both sides of the equation log base 4 of 3x = -4 with base 4?

• 3x = 64

• 3x = 16

• 3x = 256

• 3x = 1024

After finding 3x = 256, what is the final step to solve for x?

• Subtract 3 from both sides

• Add 3 to both sides

• Divide both sides by 3

• Multiply both sides by 3

What does Ln represent in logarithmic equations?

• Logarithm with base e

• Logarithm with base 2

• Logarithm with base 5

• Logarithm with base 10

In the equation 2 Ln(x) = 10, what is the first step to isolate the natural log?

• Divide both sides by 2

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 2

After isolating Ln(x) = 5, what is the next step to solve for x?

• Exponentiate both sides with base 2

• Exponentiate both sides with base 5

• Exponentiate both sides with base e

• Exponentiate both sides with base 10