How do you find the equation of the line tangent to the graph of f(x)= (ln x)^5 at x=5?

1 Answer
Feb 26, 2016

f ' (x) = 5 (ln x ) (1/x)
f ' (5) = 5 (ln 5) (1/5) = ln 5 ---- this is the slope
f(5) = (ln 5 )^5

y-(ln 5)^5 = ln 5 (x - 5)

Explanation:

Use chain rule to find derivative of f(x) and then put in 5 for x. Find the y-coordinate by putting in 5 for x in the original function then use the slope and the point to write the equation of a tangent line.