Exponential and Logarithmic Equations

Professor Dave explains how to solve exponential and logarithmic equations using logarithms. He starts with simple equations like 2^X = 16 and progresses to more complex ones, such as 3^(2X-7) = 27. The video covers changing bases, using natural logs, and applying properties of logarithms to solve equations. The tutorial also includes solving polynomial equations derived from logarithmic expressions.

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

• 2

• 5

• 4

• 3

How can we solve 2^X = 17 using logarithms?

• By guessing the value of X

• By dividing both sides by 2

• By multiplying both sides by 2

• By taking the log base 2 of both sides

What is the precise solution for X in 2^X = 17?

• X = log base 2 of 17

• X = 17

• X = 4

• X = 2

How can we express 3^(2X-7) = 27 in terms of the same base?

• By expressing 27 as 3^2

• By expressing 27 as 3^4

• By expressing 27 as 3^3

• By expressing 27 as 3^5

What is the value of X in the equation 3^(2X-7) = 27?

• X = 3

• X = 4

• X = 5

• X = 6

How do we solve 2^(X+3) = 4^(X-1) by changing the base?

• By expressing 4 as 2^5

• By expressing 4 as 2^4

• By expressing 4 as 2^3

• By expressing 4 as 2^2

What is the value of X in the equation 2^(X+3) = 4^(X-1)?

• X = 3

• X = 4

• X = 6

• X = 5

What is the first step in solving 2^(X+3) = 4^(X-1)?

• Express 4 as 2^3

• Express 4 as 2^4

• Express 4 as 2^2

• Express 4 as 2^5

What is the first step in solving 2^(X+3) = 4^(X-1)?

• Express 4 as 2^2

• Express 4 as 2^4

• Express 4 as 2^5

• Express 4 as 2^3

How do we solve 3^(X+2) = 2^(X-1) when the bases cannot be made the same?

• By guessing the value of X

• By taking the log base 2 of both sides

• By taking the log base 3 of both sides

• By taking the natural log of both sides