Answer
$$y = \frac{x}{{10\ln 10}} - \frac{1}{{\ln 10}} + 1$$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = \log x{\text{ and the point }}{x_0} = 10 \cr
& {\text{then }}f\left( {{x_0}} \right) = \log 10 = 1 \cr
& {\text{we have the point}}\left( {10,1} \right) \cr
& {\text{Find the derivative of }}f\left( x \right) \cr
& f'\left( x \right) = \left( {\log x} \right)' \cr
& f'\left( x \right) = \frac{1}{{x\ln 10}} \cr
& {\text{evaluate }}f'\left( x \right){\text{ at the point }}{x_0}{\text{ to find the slope}} \cr
& f'\left( {10} \right) = \frac{1}{{10\ln 10}} \cr
& {\text{then }}m = \frac{1}{{10\ln 10}} \cr
& \cr
& {\text{using the equation of the point - slope form }}y - {y_1} = m\left( {x - {x_1}} \right),{\text{ point }}\left( {10,1} \right) \cr
& y - 1 = \frac{1}{{10\ln 10}}\left( {x - 10} \right) \cr
& {\text{Simplify}} \cr
& y - 1 = \frac{x}{{10\ln 10}} - \frac{1}{{\ln 10}} \cr
& y = \frac{x}{{10\ln 10}} - \frac{1}{{\ln 10}} + 1 \cr} $$
