Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 527: 48

$x \approx 2.742$

$7(2.5)^{x} + 12 = 4(2.5)^{x} + 49$ $7(2.5)^{x} - 4(2.5)^{x} = 49 - 12$ $(7-4)(2.5)^{x} = 37$ $3(2.5)^{x} = 37$ $(2.5)^{x} = \frac{37}{3}$ $x = \log_{2.5} (\frac{37}{3})$ $x = \frac{\log (\frac{37}{3})}{\log 2.5}$ by GDC / calculator $x = 2.74182...$ $x \approx 2.742$