Solving Logarithmic Equations Challenge

The video tutorial covers solving logarithmic equations, starting with an introduction to the topic and the properties of logarithms. It explains the log loop and the importance of checking for extraneous solutions. The tutorial provides four examples, each demonstrating different scenarios: a single logarithm, two logarithms, three logarithms, and subtraction of logarithms. Each example is solved step-by-step, emphasizing the need to verify solutions to ensure they are not extraneous.

What is the first step in solving a logarithmic equation?

• Condense the logarithms into a single log

• Add all the logarithms together

• Convert the logarithm to exponential form

• Check for extraneous solutions

What does the log loop help you do?

• Add logarithms together

• Multiply logarithms

• Convert a logarithmic equation to an exponential equation

• Subtract logarithms

In Example A, what is the value of x when solving 4^2 = x + 3?

• 8

• 13

• 16

• 3

Why do we check for extraneous solutions in logarithmic equations?

• To ensure the argument is greater than zero

• To verify the base of the logarithm

• To simplify the equation

• To find the exact value of x

In Example B, what is the correct solution for the equation after condensing the logarithms and solving?

• x = -1

• x = 0

• x = 8

• x = 8 and x = -1

What happens to the solution x = -1 in Example B?

• It is a valid solution

• It is an extraneous solution

• It is the only solution

• It is ignored

In Example C, what is the base of the natural logarithm used in the log loop?

• 2

• 10

• e

• 1

What are the solutions found in Example C before checking for extraneous solutions?

• x = 1/4 and x = 7

• x = -1/4 and x = 7

• x = 1/4 and x = -7

• x = -1/4 and x = -7

In Example D, what is the final value of x after solving the equation 8 = (x + 2) / (x - 5)?

• 7

• 8

• 6

• 5

What must be true for the arguments in logarithmic equations to ensure the solution is not extraneous?

• The arguments must be less than zero

• The arguments must be equal to zero

• The arguments must be negative

• The arguments must be greater than zero