Solving a logarithmic equation by converting to exponential form

The video tutorial explains how to solve the equation 8^(2X-1) = 1/3 by converting it from logarithmic to exponential form. It covers the concept of rational exponents and root powers, demonstrating how to simplify and solve for X. The tutorial concludes with a verification step to ensure the solution is correct.

What is the first step in solving the equation 8^(2x-1) = 1/3?

• Add 1 to both sides

• Rewrite the equation in exponential form

• Multiply both sides by 2

• Convert the equation to logarithmic form

How can 8^(1/3) be expressed using roots?

• As the square root of 8

• As the fourth root of 8

• As the cube root of 8

• As the fifth root of 8

What is the cube root of 8?

• 4

• 3

• 2

• 1

What is the value of x when the equation 8^(2x-1) = 1/3 is solved?

• 1/2

• 3/2

• 2/3

• 1/3

Why is it important to check the solution of the equation?

• To simplify the equation further

• To find a different solution

• To ensure the solution is not extraneous

• To convert it back to logarithmic form