Exploring Logarithm Solutions: Part 1

This video tutorial covers solving logarithmic equations, focusing on the one-to-one property, condensing logarithms, and converting to exponential form. It includes examples demonstrating these techniques and concludes with solving equations using natural logarithms and power rules.

What is the first step in solving equations where log equals log?

• Combine the logarithms

• Use the one-to-one property

• Drop the logarithms

• Check for extraneous solutions

What does the one-to-one property allow you to do?

• Divide the logarithms

• Multiply the bases

• Set the arguments of the logarithms equal to each other

• Combine different bases

How do you solve the equation after applying the one-to-one property?

• Using substitution

• By graphing

• Solving the resulting equation

• Applying logarithmic properties

What is crucial to check after solving a logarithmic equation?

• If the solution is a prime number

• For extraneous solutions

• The base of the logarithm

• If the solution is an integer

How do you rewrite a logarithmic equation in exponential form?

• By raising the base to the power of the solution

• Subtracting the base from the logarithm

• Multiplying the base by the logarithm

• Dividing the base by the logarithm

What rule do you apply when you have log base 2 of 20 minus log base 2 of 5 equals x?

• Change of base rule

• Power rule

• Quotient rule

• Product rule

What is the result of simplifying log base 2 of 20 over 5?

• log base 2 of 4

• log base 2 of 10

• log base 2 of 15

• log base 2 of 25

What is the value of x when log base 2 of 4 equals x?

• 1

• 2

• 4

• 8

What property is used to combine natural log of e to the 12 and natural log of e to the negative 17?

• Power rule

• Product rule

• Quotient rule

• Change of base rule

What is the final value in the equation involving 3 natural log of e to the fourth plus 3 natural log of e to the negative 17?

• -12

• 12

• 5

• -5