Question

Find an equation of the tangent line to the graph of the function at the given point.

Answer 1

Step 1:

The function is and point is .

Change-of-base formula for logarithms : .

Apply derivative on each side with respect to .

.

Step 2:

Find slope at the point .

Substitute in derivative of the function.

.

Slope of a tangent line is .

Point - slope form of a line equation is .

Substitute and in point - slope form.

The tangent line equation is .

Step 3:

Graph :

Graph the function and tangent line is :

Solution :

The tangent line equation is .