If the curve `y=a^x` and `y=b^x` intersect at angle `alpha`, then `tan alpha=`

Options

A. `(a-b)/(1+ab)`
B. `(loga-logb)/(1+logalogb)`
C. `(1+b)/(1-ab)`
D. `(loga+logb)/(1-logalogb)`

Answer

B

Explanation

Given equation of curves are `y=a^(x) and y=b^(x)`
point of intersection of curves is (0,1)
Now, slope of tangent to the curve `y=a^(x)` is
`m_(1)=(dy)/(dx)=a^(x)loga`
`impliesm_(1)=((dy)/(dx))_((0,1))=loga`
Slope of tangent to the curve
`y=b^(x)` is
`m_(2)=(dy)/(dx)=b^(x)logb`
angle between two intersecting curves is given by
`tanalpha=(m_(1)-m_(2))/(1+m_(1)m_(2))=(loga-logb)/(1+logalogb)`