Logarithmic Equations and Properties

The video tutorial covers solving logarithmic equations. It begins with a review of guidelines for solving log equations, including combining logs, isolating the log, converting to exponential form, solving for the variable, and checking the answer. Two examples are provided: one involving a natural log equation and another with a common log equation. Each example demonstrates the process of solving the equation and verifying the solution.

What is the first step in solving logarithmic equations when there is more than one log?

• Isolate the log on one side

• Combine them using logarithm properties

• Convert to exponential form

• Check the answer

What is the base of a natural logarithm?

• 5

• e

• 2

• 10

In the equation ln(2x - 1) = 5, what is the exponential form?

• 5^e = 2x - 1

• e^5 = 2x - 1

• 10^5 = 2x - 1

• 2^5 = x - 1

After solving the equation ln(2x - 1) = 5, what is the approximate value of x?

• 100.5678

• 50.1234

• 74.7066

• 25.4321

What is the first step in solving the equation 2 log(x - 2) + 3 = 7?

• Multiply both sides by 2

• Subtract 3 from both sides

• Add 3 to both sides

• Divide both sides by 2

What is the base of a common logarithm?

• 2

• e

• 10

• 5

In the equation log(x - 2) = 2, what is the exponential form?

• 2^10 = x - 2

• 5^2 = x - 2

• e^2 = x - 2

• 10^2 = x - 2

What is the value of x in the equation log(x - 2) = 2?

• 102

• 106

• 100

• 104

How do you verify the solution of a logarithmic equation?

• By guessing

• By using a different base

• By solving another equation

• By checking if the solution satisfies the original equation

What is the common log of 100?

• 4

• 1

• 2

• 3