Understanding Absolute Values and Exponents

This tutorial explains how to solve an exponential equation involving the absolute value of X. The problem is transformed using the laws of indices, and the solution is derived by equating exponents. The absolute value of X is found to be 1, leading to two possible solutions: X = 1 and X = -1. These solutions are verified by substituting back into the original equation. The tutorial concludes with a verification of the solutions and an invitation to subscribe for more content.

What is the main goal of the tutorial?

• To learn about logarithms

• To solve a simple exponential equation

• To understand quadratic equations

• To find complex solutions for an equation

How can 9 be rewritten using the base 3?

• 3^3

• 3^1

• 3^2

• 3^0

What property of exponents is used to simplify the equation?

• Subtracting exponents with different bases

• Adding exponents with the same base

• Dividing exponents with the same base

• Multiplying exponents with different bases

What is the base used in the exponential equation?

• 2

• 3

• 5

• 4

What equation is formed after equating the exponents?

• |x| = 2 / |x|

• |x| = 2 - |x|

• |x| = 2 + |x|

• |x| = 2 * |x|

What is the value of |x| after solving the equation?

• 3

• 2

• 1

• 0

What are the possible values of x given |x| = 1?

• 0 and 1

• 3 and -3

• 1 and -1

• 2 and -2

Why is it necessary to test the possible values of x in the original equation?

• To verify the correctness of the solutions

• To change the base of the equation

• To simplify the equation further

• To find more solutions

What is the result when x = 1 is substituted back into the original equation?

• The right side is greater than the left side

• The equation becomes undefined

• The left side is greater than the right side

• Both sides are equal

What happens when x = -1 is substituted back into the original equation?

• Both sides are equal

• The right side is greater than the left side

• The left side is greater than the right side

• The equation becomes undefined