Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 60

$k = 3$

$4(3^{k}) - 40 = -6(3^{k}) + 230$ $4(3^{k}) + 6(3^{k}) = 230 + 40$ $(4+6)(3^{k}) = 270$ $10(3^{k}) = 270$ $3^{k} = 27$ $3^{k} = 3^{3}$ $k = 3$ Check: $4(3^{k}) - 40 \overset{?}{=} -6(3^{k}) + 230$ $4(3^{3}) - 40 \overset{?}{=} -6(3^{3}) +230$ $4(27) - 40 \overset{?}{=} -6(27) + 230$ $108 - 40 \overset{?}{=} -162 + 230$ $68 = 68$