Exponential and Logarithmic Equations

Professor Dave explains how to solve exponential and logarithmic equations. He starts with simple equations like 2^X = 16 and progresses to more complex ones, such as 3^(2X-7) = 27. The video covers using logarithms to solve equations, changing bases, and handling complex exponents. It also discusses solving logarithmic equations using properties of logs and provides examples of polynomial solutions.

What is the value of X in the equation 2^X = 16?

• 5

• 4

• 3

• 2

How can you solve the equation 2^X = 17 if you cannot do it mentally?

• Use a calculator directly

• Use logarithms

• Use a graph

• Use a table of values

In the equation 3^(2X-7) = 27, what is the value of X?

• 6

• 3

• 5

• 4

When solving 2^(X+3) = 4^(X-1), what is the first step to simplify the equation?

• Divide both sides by 2

• Take the natural log of both sides

• Convert 4 to 2^2

• Add 3 to both sides

What method is used to solve the equation 3^(X+2) = 2^(X-1)?

• Substitution

• Natural logarithms

• Graphical method

• Trial and error

What is the solution to the equation log base 2 of (X-4) = 3?

• 12

• 8

• 10

• 6

How do you solve log base 2 of X + log base 2 of (X-3) = 2?

• Use the power rule

• Use the change of base formula

• Use the product rule

• Use the quotient rule

What is the result of applying the product rule to log base 2 of X + log base 2 of (X-3)?

• log base 2 of (X^2 + 3X)

• log base 2 of (X - 3)

• log base 2 of (X + 3)

• log base 2 of (X^2 - 3X)

What are the solutions to the equation X^2 - 3X = 4?

• X = 3 and X = -3

• X = 4 and X = -1

• X = 5 and X = -5

• X = 2 and X = -2

Which property of logarithms allows you to combine log base 2 of X and log base 2 of (X-3)?

• Change of base formula

• Power rule

• Product rule

• Quotient rule