Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4 - Page 490: 83

$x = \frac{2}{9}$ $x = 0.22$

$\log (x+4) - \log 2 = \log (5x+1)$ $\log \frac{x+4}{2} = \log (5x+1)$ $\log \frac{x+4}{2} - \log (5x+1) = 0$ $\log \frac{x+4}{2(5x+1)} = 0$ $1 = \frac{x+4}{2(5x+1)}$ $\frac{x+4}{2(5x+1)} = 1$ $\frac{x+4}{10x+2} = 1$ $x+4 = 1(10x+2)$ $x+4 = 10x + 2$ $x - 10x = -4 + 2$ $-9x = -2$ $x = \frac{2}{9}$ by GDC / calculator $x = 0.22$