Question

If the curve y = a^x  and x = b^x intersect at angle α, find the value of tan α.

(A) (a - b)/(1 + ab)

(B) (loga - logb)/(1 + logalogb)

(C) (a + b)/(1 - ab)

(D) (loga + logb)/(1 - logalogb)

Answer 1

Answer is (B) (loga - logb)/(1 + logalogb)

Clearly, the point of intersection of curves is (0, 1).

Now, the slope of tangent of the first curve is

The slope of the tangent of the second curve is