Logarithmic and Exponential Equations

This video tutorial covers solving equations in exponential and logarithmic forms. It begins with an introduction to the concepts, followed by detailed methods for solving exponential and logarithmic equations. The tutorial includes advanced problem-solving techniques and practical applications, such as financial calculations involving compound interest. The video emphasizes the importance of understanding the base and exponent relationships and using calculators for complex calculations.

What is the first step in solving the equation 3^x = 81?

• Divide both sides by 3

• Convert the equation to logarithmic form

• Change 81 to a base of 3

• Use a calculator to find the value of x

If e^x = 13, what is the logarithmic form of this equation?

• log_10(13) = x

• log(13) = x

• ln(13) = x

• log_e(13) = x

How do you solve the equation ln(x) = 5?

• Divide both sides by ln

• Convert to exponential form: e^5 = x

• Convert to logarithmic form: log_e(x) = 5

• Use a calculator to find ln(5)

What is the solution to the equation 10^-3 = x?

• x = -1000

• x = 1/10

• x = 1000

• x = 1/1000

When solving e^(2x) = 12, what is the first step?

• Convert to logarithmic form

• Divide both sides by 2

• Subtract 12 from both sides

• Factor the equation

What is the solution to the equation e^x = 3?

• x = e^3

• x = 3

• x = ln(3)

• x = 1/3

Why can't you take the natural log of a negative number?

• Because the domain of the natural log function is x > 0

• Because it is undefined

• Because it results in zero

• Because it results in a complex number

If you want to double your money with a 6% interest rate, how long will it take?

• About 18.5 years

• About 11.5 years

• About 5.5 years

• About 23.5 years

What is the formula used for continuously compounding interest?

• A = Pe^(rt)

• A = P(1 - r/n)^(nt)

• A = P(1 + rt)

• A = P(1 + r/n)^(nt)

If you want to triple your money with a 6% interest rate, how long will it take?

• About 11.5 years

• About 30 years

• About 18.3 years

• About 23.1 years