Question

8: Find the points on curve y = log (x - 3) at which slope is 5.​

Answer 1

Answer:

(16/5, log(1/5))

Explanation:

Given,

Equation of a curve, y = log (x-3)

To Find,

The point at which slope = 5.

Solution,

Since, we know that the slope of a curve is equal to dy/dx

Here we are given that

m = dy/dx = 5

dy/dx = d(log(x-3))/dx

5 = 1/(x-3)

5x - 16 = 1

x = 16/5

Now, substituting it in the given equation

y = log (16/5 - 3)

y = log (1/5)

Hence, the point at which the slope is 5 is (16/5, log(1/5)).