Answer
$y=(\ln5)x-2\ln5+1$
Work Step by Step
$y=5^{x-2}$
$lny=ln5^{x-2}$
$=(x-2)ln5$
$lny=xln5-2ln5$
$\frac{dy}{y}=(ln5)dx$
$\frac{dy}{dx}=(ln5)y$
$=(ln5)e^{x-2}$
at (2,1),
$\frac{dy}{dx}=(ln5)5^{2-2}$
$\frac{dy}{dx}=M=ln5$
Equation of Tangent:
$(y-1)=ln5(x-2)$
$y-1=xln5-2ln5$
$y=(\ln5)x-2\ln5+1$