Write the equation of a tangent line of a natural logarithmic equation at a value

The video tutorial explains how to solve an equation involving three unknowns: X, Y, and M. It begins by identifying these unknowns and proceeds to find the values of X and Y using a given function. The tutorial then explains how to calculate the derivative, M, using logarithmic properties. Finally, it demonstrates how to set up the final equation with the known values, providing guidance on how to handle open response and multiple-choice scenarios.

What are the three unknowns in the line equation y - Y1 = m * (X - X1)?

• P, Q, and R

• L, M, and N

• A, B, and C

• X, Y, and M

If X1 is given as 2, how do you find Y using the function y = ln(2X)?

• By substituting X1 into the function

• By dividing the function by 2

• By adding 2 to the function

• By multiplying the function by 2

What is the value of Y1 when X is substituted into the function y = ln(2X)?

• ln(2)

• ln(4)

• ln(8)

• ln(6)

What is the derivative, M, in the context of the line equation?

• W prime

• Y prime

• Z prime

• X prime

How is Y prime calculated from the function y = ln(2X)?

• X

• X/2

• 2/X

• 1/X