Solving Exponential Equations with Laws of Exponents

The video tutorial covers solving exponential equations by using properties of exponents. It begins with an introduction to the topic, followed by a step-by-step guide on isolating coefficients, applying exponent properties, rewriting equations into logarithmic form, and solving for unknowns. Two example problems are provided, including a real-life word problem, to illustrate the application of these steps. The tutorial concludes with a summary of the key points discussed.

What is the first step in solving an exponential equation?

• Solve for the unknown variable

• Convert the equation to logarithmic form

• Isolate the coefficients and exponentials separately

• Apply the properties of exponents

What operation is used to separate coefficients and exponentials connected by multiplication?

• Addition

• Subtraction

• Division

• Multiplication

When dividing exponentials with the same base, what should you do with the exponents?

• Subtract them

• Multiply them

• Add them

• Divide them

What is the opposite operation of exponentiation?

• Multiplication

• Division

• Logarithm

• Addition

How do you bring down an exponent in an exponential equation?

• By subtracting the same number from both sides

• By multiplying both sides by the same number

• By applying logarithms to both sides

• By adding the same number to both sides

What is the natural logarithm of e (ln(e)) equal to?

• e

• 10

• 0

• 1

What is the approximate value of ln(4/3) divided by 3?

• 0.67890

• 0.56789

• 0.12345

• 0.09589

In the word problem, what is the initial population of Jacksonville in 2013?

• 750

• 1700

• 2000

• 3000

What is the annual population growth rate of Smithtown?

• 7.5%

• 5%

• 3%

• 10%

Approximately how many years will it take for the populations of Jacksonville and Smithtown to be equal?

• 10.5 years

• 15.2 years

• 25.3 years

• 19.1 years