Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 527: 40

$x \approx -1.324$

$7(1.8)^{3x+5} = 12.8$ $(1.8)^{3x+5} = \frac{12.8}{7}$ $3x + 5 = \log_{1.8} (\frac{12.8}{7})$ $3x = \log_{1.8} (\frac{12.8}{7}) - 5$ $x = \frac{\log_{1.8} (\frac{12.8}{7}) - 5}{3}$ $x = \frac{ (\frac{\log (\frac{12.8}{7})}{\log 1.8})- 5}{3}$ by GDC / calculator $x = -1.324402...$ $x \approx -1.324$