Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 362: 62

$y=\frac{x}{5ln10}-\frac{1}{ln10}+1$

$y=\frac{ln(2x)}{ln10}$ $=\frac{1}{ln10}ln(2x)$ $y'=\frac{1}{ln10}\frac{2}{2x}$ $=\frac{1}{ln10}$ $y'(5)=M=\frac{1}{5ln10}$ Equation of tangent: $(y-1)=\frac{1}{5ln10}(x-5)$ $y=\frac{x}{5ln10}-\frac{1}{ln10}+1$