Logarithmic and Exponential Problem Solving

This video tutorial covers solving logarithmic word problems, similar to exponential problems but without a universal formula. It includes examples using box office revenues from Finding Nemo and Terminator 3, and a sound level problem. The tutorial explains how to set up and solve logarithmic equations, emphasizing the importance of understanding the limited domain of logarithms.

What is the main difference between solving logarithmic and exponential word problems?

• Exponential problems are more complex.

• Logarithmic problems have a universal formula.

• Exponential problems are easier to solve.

• Logarithmic problems lack a universal formula.

In the Finding Nemo example, what is the first step to solve the logarithmic equation?

• Add 105.3 to both sides.

• Subtract 105.3 from both sides.

• Divide both sides by 78.05.

• Multiply both sides by 78.05.

How many weeks after the opening did Finding Nemo reach $300 million in revenue?

• 11.2 weeks

• 10.5 weeks

• 9.8 weeks

• 8.5 weeks

In the Terminator 3 example, what is the value of X when the revenue reaches $140 million?

• 5.5 weeks

• 6.5 weeks

• 7.5 weeks

• 8.5 weeks

What is the purpose of exponentiating both sides in the Terminator 3 example?

• To find the value of E.

• To simplify the equation.

• To cancel out the logarithm.

• To isolate the variable X.

In the sound level example, what is the formula used to express decibels?

• D = 10 log (P2 / P1)

• D = 20 log (P1 / P2)

• D = 20 log (P2 / P1)

• D = 10 log (P1 / P2)

What is the value of P1 when P2 is 75 watts and D is 0.7 decibels?

• 85.12 watts

• 88.12 watts

• 90.12 watts

• 92.12 watts

What mathematical operation is used to solve for P1 in the sound level example?

• Addition

• Subtraction

• Division

• Exponentiation

Why is it important to express P1 and P2 in the same units in the sound level example?

• To make the equation easier to understand.

• To avoid unit conversion errors.

• To simplify the logarithmic equation.

• To ensure accuracy in calculations.

What should students do if they have questions about the material?

• Wait for the next video.

• Ask the teacher for clarification.

• Search online for answers.

• Ignore their questions.