Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 59

$w = 3$

$13(7^{w}) + 20 = 5(7^{w}) + 2764$ $13(7^{w}) - 5(7^{w}) = 2764 - 20$ $(13-5)(7^{w}) = 2744$ $8(7^{w}) = 2744$ $7^{w} = 343$ $7^{w} = 7^{3}$ $w = 3$ Check: $13(7^{w}) + 20 \overset{?}{=} 5(7^{w}) + 2764$ $13(7^{3}) + 20 \overset{?}{=} 5(7^{3}) + 2764$ $13(343) + 20 \overset{?}{=} 5(343) + 2764$ $4459 + 20 \overset{?}{=} 1715 + 2764$ $4479 = 4479$