Solving Logarithmic Equations: Part 2 Challenge

The video tutorial covers solving logarithm equations where a log equals a number. It explains the process of condensing logarithms, converting them to exponential form, and solving for variables. The tutorial includes four examples, demonstrating the use of power and quotient rules, handling natural logarithms, and solving equations with variables on both sides. Each example concludes with a mental check to verify the solution.

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

• Isolate the logarithm

• Check for extraneous solutions

• Combine all logs on one side if necessary

• Convert to exponential form immediately

In the equation 2 log base 3 of X minus log base 3 of 4 equals 2, what rule is applied first?

• Product rule

• Power rule

• Change of base rule

• Quotient rule

After applying the power rule and quotient rule, what is the next step in solving the equation?

• Apply the change of base rule

• Simplify the equation

• Convert to exponential form

• Isolate the variable X

What is the solution to the equation log base 100 of 15 minus 4n equals one over 2?

• n = -5

• n = 5

• n = -5/4

• n = 5/4

Tags

CCSS.HSF.BF.B.5

What is the base of any natural logarithm?

• 10

• 2

• E

• 1

What is the value of E to the power of 0?

• Undefined

• E

• 1

• 0

In the final example, what operation is performed first to start solving the equation?

• Applying the quotient rule

• Subtracting log base 3 of X minus one from both sides

• Converting to exponential form

• Multiplying both sides by X minus one

Tags

CCSS.8.EE.A.2

What is the result of 3 squared in the final example?

• 18

• 12

• 6

• 9

Tags

CCSS.7.EE.B.4A

What is the final value of X in the last example?

• 4

• 3

• 2

• 1

Why is it important to perform a mental check after solving a logarithmic equation?

• To decide if the quotient rule was applied correctly

• To ensure the solution satisfies the original equation

• To verify the base of the logarithm

• To check if the logarithm is isolated