Using the one to one property to solve a logarithmic equation

The video tutorial explains how to solve a logarithmic equation using the one-to-one property. It starts with an equation involving logarithms with the same base and demonstrates how to equate the arguments. The solution is found by simplifying the equation and verifying the result by substituting it back into the original equation.

What property is used when two logarithms with the same base are equal?

• Exponential Property

• Quotient Property

• One-to-One Property

• Product Property

If log(5X) = log(2X + 9), what equation can be derived from this?

• 5X = 9 + 2X

• 5X = 2X - 9

• 5X = 2X + 9

• 5X = 9 - 2X

What is the value of X when solving the equation 5X = 2X + 9?

• X = 4

• X = 1

• X = 2

• X = 3

Why is it important to substitute the solution back into the original logarithmic expressions?

• To verify the solution satisfies the original equation

• To check if the solution is a prime number

• To find the base of the logarithms

• To determine if the solution is negative

What should you do if the substituted solution does not satisfy the original logarithmic equation?

• Use a different mathematical property

• Change the base of the logarithms

• Recalculate the solution

• Ignore the solution