Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 527: 47

$x \approx 2.268$

$5(4.3)^{x} + 7 = 2(4.3)^{x} + 89$ $5(4.3)^{x} - 2(4.3)^{x} = 89 - 7$ $(5-2)(4.3)^{x} = 82$ $3(4.3)^{x} = 82$ $(4.3)^{x} = \frac{82}{3}$ $x = \log_{4.3} (\frac{82}{3})$ $x = \frac{\log \frac{82}{3}}{\log 4.3}$ by GDC / calculator $x = 2.2679...$ $x \approx 2.268$