Find the x intercept of the tangent line to y = ln (x) with slope 46. Give your answer to 2 decimal places.

Answer 1

The slope of the tangent line is the derivative of the function.

y' = 1/x

for 1/x = 46, x = 1/46

If y = ln(x) then for x = 1/46, y = ln(1/46) or y = -3.82864 so the point on the curve of y = ln(x) where the slope is 46 is (1/46, -3.82864)

Using the point slope form of a line, the equation of this line is y - (-3.82864) = 46(x - 1/46)

The x-intercept is where y = 0

0 - (-3.82864) = 46(x - 1/46)

0 + 3.82864) = 46x - 1

4.82864 = 46x

x = 0.10

So the x-intercept is (0.10, 0)