Logarithmic and Exponential Concepts

This video tutorial explains how to solve exponential equations using common logarithms. It begins with an example of student population growth and introduces the concept of common logarithms. The tutorial then outlines the steps to solve exponential equations, including isolating the exponential part, taking the logarithm of both sides, and using the exponent property of logarithms. A second example demonstrates how inflation affects the value of money over time, reinforcing the application of logarithms in real-world scenarios.

What is the initial student population in the given example?

• 6,000

• 5,000

• 4,000

• 3,000

How is the growth rate expressed in the exponential equation?

• As a decimal

• As a whole number

• As a percentage

• As a fraction

What is the base of a common logarithm?

• 10

• 5

• 2

• e

Which property of logarithms allows the exponent to be moved to the front?

• Quotient Property

• Product Property

• Exponent Property

• Change of Base Property

What is the first step in solving an exponential equation using logarithms?

• Take the log of both sides

• Divide by the logarithm

• Isolate the exponential part

• Apply the exponent property

In the student population example, what is the approximate time for the population to reach 5,000?

• 4.57 years

• 3.57 years

• 6.57 years

• 5.57 years

What is the rate of inflation decrease in the second example?

• 1%

• 3%

• 2%

• 4%

How much will $100 be worth in 15 years according to the inflation example?

• $63.86

• $93.86

• $73.86

• $83.86

What is the equation setup to find when $100 is worth $50?

• 50 = 100 x 1.02^N

• 50 = 100 x 0.98^N

• 50 = 100 x 1.05^N

• 50 = 100 x 0.95^N

Approximately how many years will it take for $100 to be worth $50?

• 34.31 years

• 54.31 years

• 24.31 years

• 44.31 years