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, such as 3^(2X-7) = 27. He demonstrates using logarithms to solve equations where the exponent is not obvious, and explains the change-of-base property. The video also covers solving equations with different bases and using natural logs. Finally, Professor Dave addresses solving logarithmic equations using properties of logs and solving polynomials.

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

• 2

• 3

• 5

• 4

How can you solve 2^X = 17 if you cannot calculate it mentally?

• Use a calculator directly

• Use the cube root of both sides

• Use the square root of both sides

• Use the log base 2 of both sides

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

• 6

• 5

• 4

• 3

When solving 3^(X+2) = 2^(X-1), what method is used?

• Changing the base to 10

• Using natural logarithms

• Using the square root

• Using the cube root

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

• 2.5

• 1.5

• 4.5

• 3.5

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

• 6

• 12

• 10

• 8

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

• Use the power rule

• Use the quotient rule

• Use the product rule

• Use the sum 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^2-3X)

• log base 2 of (X-3)

• log base 2 of (X+3)

What is the value of X in the equation X^2 - 3X = 4?

• 4 and -1

• 3 and 1

• 2 and -2

• 5 and 0

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

• Quotient rule

• Power rule

• Product rule

• Change of base rule