Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 526: 27

$m \approx 7.600$

$-3(2.5)^{m} - 89 = -3262$ $-3(2.5)^{m} = -3262 + 89$ $-3(2.5)^{m} = -3173$ $(2.5)^{m} = 1057.666...$ $m = \log_{2.5} (1057.66...)$ $m = \frac{\log (1057.666...)}{\log (2.5)}$ by GDC / calculator $m = 7.6000...$ $m \approx 7.600$