Logarithmic Equations and Exponential Forms

The video tutorial explains how to solve logarithmic equations by converting them into exponential equations. It covers three examples: solving log base x of 27 equals 3, log base x of 256 equals 4, and a log equation with a negative exponent. The process involves using cube roots and fourth roots to find the base x. The tutorial emphasizes the importance of considering only positive solutions for the base of logarithms.

What is the first step in solving a logarithmic equation?

• Convert it to a polynomial equation

• Convert it to a linear equation

• Convert it to an exponential equation

• Convert it to a quadratic equation

If log base x of 27 equals 3, what is the value of x?

• 2

• 1

• 4

• 3

What operation is used to solve x cubed equals 27?

• Fourth root

• Fifth root

• Cube root

• Square root

In the equation log base x of 256 equals 4, what is the corresponding exponential form?

• x^3 = 256

• x^4 = 256

• x^2 = 256

• x^5 = 256

What is the value of x in the equation log base x of 256 equals 4?

• 2

• 3

• 4

• 5

What is the prime factorization of 256?

• 8^2

• 4^4

• 2^4

• 2^8

In the equation log base x of 1/625 equals -4, what is the corresponding exponential form?

• x^4 = 625

• x^-4 = 625

• x^-4 = 1/625

• x^4 = 1/625

What is the value of x in the equation log base x of 1/625 equals -4?

• 6

• 5

• 4

• 3

What is the prime factorization of 625?

• 5^2

• 5^1

• 5^4

• 5^3

What is the key takeaway from solving logarithmic equations?

• Always convert to polynomial form

• Always convert to linear form

• Always convert to exponential form

• Always convert to quadratic form