Solving Logarithmic Equations Challenge

In this video, Mr. Banker explains how to solve logarithmic equations by converting them into exponential form. He discusses the one-to-one property of logarithms and demonstrates how to use logarithmic properties to simplify and solve equations. The video also covers solving quadratic equations that arise from logarithmic problems, highlighting the importance of checking for extraneous solutions.

What is the exponential form of log(x^2) = 2?

• x^2 = 2^10

• 2^10 = x^2

• 10^2 = x^2

• log(2) = x^10

What is the base of a logarithm if it is not specified?

• It is undefined

• 2

• e (Euler's Number)

• 10

What is the result of 10 squared?

• 20

• 100

• 1000

• 10

If log base 2 of x equals log base 2 of 4, what is x?

• 16

• 8

• 4

• 2

What does the one-to-one property of logarithmic equations allow you to do?

• Solve quadratic equations

• Combine logarithms

• Cancel out the logarithms and equate the arguments

• Convert logarithms to exponential form

What property allows you to combine log(x) + log(x-9) into a single logarithm?

• Change of Base Property

• Power Property

• Product Property

• Quotient Property

What is the solution to the equation 10 = x(x - 9)?

• x = -1

• x = 10, x = -1

• x = 5, x = -2

• x = 10

What is the correct way to rewrite log(x) + log(x - 9) = 1 in exponential form?

• 1^10 = x(x - 9)

• log(10) = x + x - 9

• x^10 = 1(x - 9)

• 10^1 = x(x - 9)

Why is x = -1 considered an extraneous solution in the context of logarithmic equations?

• Because it does not satisfy the original equation

• Because it makes the equation undefined

• Because it results in a negative number under a logarithm

• Because it is not a real number

How do you solve the equation x^2 - 9x - 10 = 0?

• x = 5, x = -2

• x = -10, x = 9

• x = 10, x = -1

• x = 10, x = 1