Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 53

$$ y=36((\ln 6 ) \ x+1-2\ln 6).$$

Let $ f(x)=6^x $, then $ f'(x)=6^x \ln 6$ and the slope of $ f $ at $ x=2$ is given by $$ m=f'(2)=6^2 \ln 6.$$ The equation of the tangent line $$ y=36(\ln 6) \ x+c.$$ Since the function and the tangent line coincide at $ x=2$, we have $$ c=6^2-36(\ln 6) (2)=36(1-2\ln 6).$$ Finally, we get $$ y=36((\ln 6 ) \ x+1-2\ln 6).$$