Logarithmic Equations and Properties

The video tutorial explains how to solve a logarithmic equation involving the square of log base two of x. It begins by applying the power property of logarithms and highlights the importance of recognizing when this property can be applied. The tutorial then uses substitution to simplify the equation, followed by factoring to solve it. The process involves isolating the logarithm and converting the log equations into exponential form to find the solutions. The video concludes by summarizing the two solutions obtained.

What is the initial form of the logarithmic equation presented in the video?

• log base 2 of x^4 = log base 2 of x^12

• 4 * log base 2 of x^2 = log base 2 of x^12

• 4 * (log base 2 of x)^2 = log base 2 of x^12

• 4 * log base 2 of x = log base 2 of x^12

Which property of logarithms is applied to simplify the right side of the equation?

• Product Property

• Power Property

• Change of Base Property

• Quotient Property

What substitution is made to simplify the equation for factoring?

• u = x^12

• u = x^2

• u = 4 * log base 2 of x

• u = log base 2 of x

What is the greatest common factor factored out from the equation?

• 4

• u

• 4u

• 12

Tags

CCSS.HSA-REI.B.4B

After factoring, what are the two possible equations set to zero?

• 4u = 0 and u - 3 = 0

• 4u = 0 and u + 3 = 0

• u = 0 and 4u - 3 = 0

• u = 0 and 4u + 3 = 0

Tags

CCSS.HSF.BF.B.5

How is the equation log base 2 of x = 0 converted to exponential form?

• 2^0 = x

• x^2 = 0

• 2^x = 0

• x^0 = 2

Tags

CCSS.HSF.BF.B.5

What is the solution for x when log base 2 of x = 0?

• x = 2

• x = 1

• x = 0

• x = 3

Tags

CCSS.HSF.BF.B.5

How is the equation log base 2 of x = 3 converted to exponential form?

• x^3 = 2

• 3^2 = x

• x^2 = 3

• 2^3 = x

Tags

CCSS.HSF.BF.B.5

What is the solution for x when log base 2 of x = 3?

• x = 6

• x = 12

• x = 3

• x = 8

How many solutions does the original logarithmic equation have?

• Two

• Three

• Four

• One