Solving 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, using logarithms to find solutions. The video covers changing bases, using natural logs, and solving equations with complex exponents. It also includes solving logarithmic equations using properties like the product rule.

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

• 2

• 5

• 3

• 4

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

• Use a graph

• Use a calculator directly

• Use a guess and check method

• Use logarithms

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

• 6

• 5

• 4

• 3

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

• Subtract 1 from both sides

• Add 3 to both sides

• Take the natural log of both sides

• Convert 4 to 2^2

What method is used to solve the equation 3^(X+2) = 2^(X-1) when the bases cannot be made the same?

• Use the power rule

• Take the natural log of both sides

• Use the quotient rule

• Use the product rule

What is the approximate value of X in the equation 3^(X+2) = 2^(X-1) using natural logs?

• 3.5

• 1.5

• 2.5

• 4.5

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

• 14

• 12

• 10

• 8

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

• Use the quotient rule

• Use the product rule

• Use the power rule

• Use the change of base formula

What is the solution to the polynomial X^2 - 3X = 4?

• X = 6 or X = -4

• X = 5 or X = -3

• X = 3 or X = -2

• X = 4 or X = -1

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

• Product rule

• Power rule

• Change of base formula

• Quotient rule