Solving Exponential equations

The video tutorial explains how to solve equations using one-to-one properties. It begins by emphasizing the importance of having the same base for exponents to apply these properties. The instructor demonstrates rewriting 25 as a base of 5 and explains the multiplication of exponents when raising a power. The tutorial then walks through solving the equation step-by-step, applying the one-to-one properties to equate exponents and solve for the variable. The session concludes with a summary of the process.

Why is it important to have the same base when applying one-to-one properties in exponents?

• To ensure the exponents can be compared directly

• To avoid using a calculator

• To make the equation look nicer

• To simplify the calculation

How can the number 25 be rewritten to have a base of 5?

• 5^3

• 5^2

• 5^0

• 5^1

What is the result of multiplying the exponents in the expression 5^(2*(X-6))?

• 5^(2X-12)

• 5^(X-12)

• 5^(2X-6)

• 5^(X-6)

In the equation 5^(X-4) = 5^(2X-12), what is the first step to solve for X?

• Add 4 to both sides

• Multiply both sides by 5

• Set the exponents equal to each other

• Subtract X from both sides

What is the final value of X in the equation 5^(X-4) = 5^(2X-12)?

• X = 16

• X = 12

• X = 8

• X = 4