Answer
$y=10xln10+10(1-ln10)$
Work Step by Step
Differentiate $y=10^{x}$ with respect to $x$.
$y'=10^{x}ln10$
Let $m$ be the slope of tangent of the line passing through the points (1, 10).
$m|_{(1, 10)}=10^{1}ln10 =10 ln10$
The equation of the tangent of the line passing through the points (1, 10) is
$(y-10)=10ln10(x-1)$
Hence, $y=10xln10+10(1-ln10)$